diff --git a/bilby/core/result.py b/bilby/core/result.py
index 48797a4f100e6583a880b59822df61997c6aeaa8..e2608932ed2ab71f9ff8ca11ca659d4a81b74cfc 100644
--- a/bilby/core/result.py
+++ b/bilby/core/result.py
@@ -422,65 +422,6 @@ class Result(object):
         self.prior_values = None
         self._kde = None
 
-    @classmethod
-    def _from_hdf5_old(cls, filename=None, outdir=None, label=None):
-        """ Read in a saved .h5 data file in the old format.
-
-        Parameters
-        ==========
-        filename: str
-            If given, try to load from this filename
-        outdir, label: str
-            If given, use the default naming convention for saved results file
-
-        Returns
-        =======
-        result: bilby.core.result.Result
-
-        Raises
-        =======
-        ValueError: If no filename is given and either outdir or label is None
-                    If no bilby.core.result.Result is found in the path
-
-        """
-        import deepdish
-        filename = _determine_file_name(filename, outdir, label, 'hdf5', False)
-
-        if os.path.isfile(filename):
-            dictionary = deepdish.io.load(filename)
-            # Some versions of deepdish/pytables return the dictionary as
-            # a dictionary with a key 'data'
-            if len(dictionary) == 1 and 'data' in dictionary:
-                dictionary = dictionary['data']
-
-            if "priors" in dictionary:
-                # parse priors from JSON string (allowing for backwards
-                # compatibility)
-                if not isinstance(dictionary["priors"], PriorDict):
-                    try:
-                        priordict = PriorDict()
-                        for key, value in dictionary["priors"].items():
-                            if key not in ["__module__", "__name__", "__prior_dict__"]:
-                                try:
-                                    priordict[key] = decode_bilby_json(value)
-                                except AttributeError:
-                                    continue
-                        dictionary["priors"] = priordict
-                    except Exception as e:
-                        raise IOError(
-                            "Unable to parse priors from '{}':\n{}".format(
-                                filename, e,
-                            )
-                        )
-            try:
-                if isinstance(dictionary.get('posterior', None), dict):
-                    dictionary['posterior'] = pd.DataFrame(dictionary['posterior'])
-                return cls(**dictionary)
-            except TypeError as e:
-                raise IOError("Unable to load dictionary, error={}".format(e))
-        else:
-            raise IOError("No result '{}' found".format(filename))
-
     _load_doctstring = """ Read in a saved .{format} data file
 
     Parameters
@@ -516,8 +457,6 @@ class Result(object):
         filename = _determine_file_name(filename, outdir, label, 'hdf5', False)
         with h5py.File(filename, "r") as ff:
             data = recursively_load_dict_contents_from_group(ff, '/')
-        if list(data.keys()) == ["data"]:
-            return cls._from_hdf5_old(filename=filename)
         data["posterior"] = pd.DataFrame(data["posterior"])
         data["priors"] = PriorDict._get_from_json_dict(
             json.loads(data["priors"], object_hook=decode_bilby_json)
diff --git a/bilby/core/utils/__init__.py b/bilby/core/utils/__init__.py
index 85c3fb1f4d04df7bb994c17d10659e9a86eb7b76..10509641a3e71b10620e51ba3ec98ca788b6e9d7 100644
--- a/bilby/core/utils/__init__.py
+++ b/bilby/core/utils/__init__.py
@@ -9,7 +9,6 @@ from .introspection import *
 from .io import *
 from .log import *
 from .plotting import *
-from .progress import *
 from .samples import *
 from .series import *
 
diff --git a/bilby/core/utils/conversion.py b/bilby/core/utils/conversion.py
index 978e34346039d2d7fafb1cc865349394cb25969e..c89e2a9ec6210bd73c2816ab237f319a86e24bbc 100644
--- a/bilby/core/utils/conversion.py
+++ b/bilby/core/utils/conversion.py
@@ -1,6 +1,3 @@
-import warnings
-from math import fmod
-
 import numpy as np
 
 
@@ -31,53 +28,3 @@ def theta_phi_to_ra_dec(theta, phi, gmst):
     ra = phi + gmst
     dec = np.pi / 2 - theta
     return ra, dec
-
-
-def gps_time_to_gmst(gps_time):
-    """
-    Convert gps time to Greenwich mean sidereal time in radians
-
-    This method assumes a constant rotation rate of earth since 00:00:00, 1 Jan. 2000
-    A correction has been applied to give the exact correct value for 00:00:00, 1 Jan. 2018
-    Error accumulates at a rate of ~0.0001 radians/decade.
-
-    Parameters
-    ----------
-    gps_time: float
-        gps time
-
-    Returns
-    -------
-    float: Greenwich mean sidereal time in radians
-
-    """
-    warnings.warn(
-        "Function gps_time_to_gmst deprecated, use "
-        "lal.GreenwichMeanSiderealTime(time) instead",
-        DeprecationWarning)
-    omega_earth = 2 * np.pi * (1 / 365.2425 + 1) / 86400.
-    gps_2000 = 630720013.
-    gmst_2000 = (6 + 39. / 60 + 51.251406103947375 / 3600) * np.pi / 12
-    correction_2018 = -0.00017782487379358614
-    sidereal_time = omega_earth * (gps_time - gps_2000) + gmst_2000 + correction_2018
-    gmst = fmod(sidereal_time, 2 * np.pi)
-    return gmst
-
-
-def spherical_to_cartesian(radius, theta, phi):
-    """ Convert from spherical coordinates to cartesian.
-
-    Parameters
-    ==========
-    radius: float
-        radial coordinate
-    theta: float
-        axial coordinate
-    phi: float
-        azimuthal coordinate
-
-    Returns
-    =======
-    list: cartesian vector
-    """
-    return [radius * np.sin(theta) * np.cos(phi), radius * np.sin(theta) * np.sin(phi), radius * np.cos(theta)]
diff --git a/bilby/core/utils/progress.py b/bilby/core/utils/progress.py
deleted file mode 100644
index 9db1752b2c63204c3f881e00f45385e4e04a10d0..0000000000000000000000000000000000000000
--- a/bilby/core/utils/progress.py
+++ /dev/null
@@ -1,18 +0,0 @@
-def get_progress_bar(module='tqdm'):
-    """
-    TODO: Write proper docstring
-    """
-    if module in ['tqdm']:
-        try:
-            from tqdm import tqdm
-        except ImportError:
-            def tqdm(x, *args, **kwargs):
-                return x
-        return tqdm
-    elif module in ['tqdm_notebook']:
-        try:
-            from tqdm import tqdm_notebook as tqdm
-        except ImportError:
-            def tqdm(x, *args, **kwargs):
-                return x
-        return tqdm
diff --git a/bilby/gw/detector/interferometer.py b/bilby/gw/detector/interferometer.py
index 8447c16eff482fa3a1abb00d4e5bfd0ecd52a354..06b298386e3d2d8a8887f89af3d65f3e58919efd 100644
--- a/bilby/gw/detector/interferometer.py
+++ b/bilby/gw/detector/interferometer.py
@@ -771,32 +771,6 @@ class Interferometer(object):
 
     """
 
-    @docstring(_save_ifo_docstring.format(
-        format="hdf5", extra=""".. deprecated:: 1.1.0
-    Use :func:`to_pickle` instead."""
-    ))
-    def to_hdf5(self, outdir='outdir', label=None):
-        import deepdish
-        if label is None:
-            label = self.name
-        utils.check_directory_exists_and_if_not_mkdir('outdir')
-        try:
-            filename = self._filename_from_outdir_label_extension(outdir, label, "h5")
-            deepdish.io.save(filename, self)
-        except AttributeError:
-            logger.warning("Saving to hdf5 using deepdish failed. Pickle dumping instead.")
-            self.to_pickle(outdir=outdir, label=label)
-
-    @classmethod
-    @docstring(_load_docstring.format(format="hdf5"))
-    def from_hdf5(cls, filename=None):
-        import deepdish
-
-        res = deepdish.io.load(filename)
-        if res.__class__ != cls:
-            raise TypeError('The loaded object is not an Interferometer')
-        return res
-
     @docstring(_save_ifo_docstring.format(
         format="pickle", extra=".. versionadded:: 1.1.0"
     ))
diff --git a/bilby/gw/detector/networks.py b/bilby/gw/detector/networks.py
index db0d4743b148338b49590a59c067e9f3f2cc97d9..4f03b948b7079f4abb085b8d4920e437c2683280 100644
--- a/bilby/gw/detector/networks.py
+++ b/bilby/gw/detector/networks.py
@@ -272,31 +272,6 @@ class InterferometerList(list):
 
     """
 
-    def to_hdf5(self, outdir="outdir", label="ifo_list"):
-        import deepdish
-
-        label = label + "_" + "".join(ifo.name for ifo in self)
-        utils.check_directory_exists_and_if_not_mkdir(outdir)
-        try:
-            filename = self._filename_from_outdir_label_extension(outdir, label, "h5")
-            deepdish.io.save(filename, self)
-        except AttributeError:
-            logger.warning(
-                "Saving to hdf5 using deepdish failed. Pickle dumping instead."
-            )
-            self.to_pickle(outdir=outdir, label=label)
-
-    @classmethod
-    def from_hdf5(cls, filename=None):
-        import deepdish
-
-        res = deepdish.io.load(filename)
-        if res.__class__ == list:
-            res = cls(res)
-        if res.__class__ != cls:
-            raise TypeError("The loaded object is not a InterferometerList")
-        return res
-
     def to_pickle(self, outdir="outdir", label="ifo_list"):
         import dill
 
@@ -318,15 +293,9 @@ class InterferometerList(list):
             raise TypeError("The loaded object is not an InterferometerList")
         return res
 
-    to_hdf5.__doc__ = _save_docstring.format(
-        format="hdf5",
-        extra=""".. deprecated:: 1.1.0
-    Use :func:`to_pickle` instead.""",
-    )
     to_pickle.__doc__ = _save_docstring.format(
         format="pickle", extra=".. versionadded:: 1.1.0"
     )
-    from_hdf5.__doc__ = _load_docstring.format(format="hdf5")
     from_pickle.__doc__ = _load_docstring.format(format="pickle")
 
 
diff --git a/bilby/gw/likelihood/base.py b/bilby/gw/likelihood/base.py
index 55845c09372222b48f83e15d862dbd95c9f13ae8..d4d8eca345bb8f6dfca921f4cd20bfcbc3c5cb6c 100644
--- a/bilby/gw/likelihood/base.py
+++ b/bilby/gw/likelihood/base.py
@@ -936,15 +936,6 @@ class GravitationalWaveTransient(Likelihood):
             "to use bilby.gw.utils.ln_i0"
         )
 
-    @staticmethod
-    def _bessel_function_interped(xx):
-        logger.warning(
-            "The _bessel_function_interped method is deprecated and will be removed, "
-            "please update the implementation of phase marginalization "
-            "to use bilby.gw.utils.ln_i0"
-        )
-        return ln_i0(xx) + xx
-
     def _setup_time_marginalization(self):
         self._delta_tc = 2 / self.waveform_generator.sampling_frequency
         self._times = \
diff --git a/test/gw/detector/interferometer_test.py b/test/gw/detector/interferometer_test.py
index 2a37830fcfec33bd1dab8e8df1cca41e4b9c4ca1..3eea3c59d4667bd3fad5232bfb866ca5b98b636d 100644
--- a/test/gw/detector/interferometer_test.py
+++ b/test/gw/detector/interferometer_test.py
@@ -3,13 +3,9 @@ from unittest import mock
 
 import lal
 import lalsimulation
-import pytest
-from packaging import version
 from shutil import rmtree
 
-import deepdish as dd
 import numpy as np
-import pandas
 
 import bilby
 
@@ -371,28 +367,6 @@ class TestInterferometer(unittest.TestCase):
         )
         self.assertEqual(expected, repr(self.ifo))
 
-    pandas_version_test = version.parse(pandas.__version__) >= version.parse("1.2.0")
-    skip_reason = "Deepdish requires pandas < 1.2"
-
-    @pytest.mark.skipif(pandas_version_test, reason=skip_reason)
-    def test_to_and_from_hdf5_loading(self):
-        self.ifo.to_hdf5(outdir="outdir", label="test")
-        filename = self.ifo._filename_from_outdir_label_extension(
-            outdir="outdir", label="test", extension="h5"
-        )
-        recovered_ifo = bilby.gw.detector.Interferometer.from_hdf5(filename)
-        self.assertEqual(self.ifo, recovered_ifo)
-
-    @pytest.mark.skipif(pandas_version_test, reason=skip_reason)
-    def test_to_and_from_hdf5_wrong_class(self):
-        bilby.core.utils.check_directory_exists_and_if_not_mkdir("outdir")
-        dd.io.save("./outdir/psd.h5", self.power_spectral_density)
-        filename = self.ifo._filename_from_outdir_label_extension(
-            outdir="outdir", label="psd", extension="h5"
-        )
-        with self.assertRaises(TypeError):
-            bilby.gw.detector.Interferometer.from_hdf5(filename)
-
     def test_to_and_from_pkl_loading(self):
         self.ifo.to_pickle(outdir="outdir", label="test")
         filename = "outdir/test.pkl"
diff --git a/test/gw/detector/networks_test.py b/test/gw/detector/networks_test.py
index 971254b24f425a79e333fda6a57c464d75dfbbf2..744d872a114505a1db56460186e985d961c8a10b 100644
--- a/test/gw/detector/networks_test.py
+++ b/test/gw/detector/networks_test.py
@@ -1,13 +1,9 @@
 import unittest
 from unittest import mock
-import pytest
 from shutil import rmtree
-from packaging import version
 from itertools import combinations
 
-import deepdish as dd
 import numpy as np
-import pandas
 
 import bilby
 
@@ -326,25 +322,6 @@ class TestInterferometerList(unittest.TestCase):
         names = [ifo.name for ifo in self.ifo_list]
         self.assertListEqual([self.ifo1.name, new_ifo.name, self.ifo2.name], names)
 
-    pandas_version_test = version.parse(pandas.__version__) >= version.parse("1.2.0")
-    skip_reason = "Deepdish requires pandas < 1.2"
-
-    @pytest.mark.skipif(pandas_version_test, reason=skip_reason)
-    def test_to_and_from_hdf5_loading(self):
-        self.ifo_list.to_hdf5(outdir="outdir", label="test")
-        filename = "outdir/test_name1name2.h5"
-        recovered_ifo = bilby.gw.detector.InterferometerList.from_hdf5(filename)
-        self.assertListEqual(self.ifo_list, recovered_ifo)
-
-    @pytest.mark.skipif(pandas_version_test, reason=skip_reason)
-    def test_to_and_from_hdf5_wrong_class(self):
-        dd.io.save("./outdir/psd.h5", self.ifo_list[0].power_spectral_density)
-        filename = self.ifo_list._filename_from_outdir_label_extension(
-            outdir="outdir", label="psd", extension="h5"
-        )
-        with self.assertRaises(TypeError):
-            bilby.gw.detector.InterferometerList.from_hdf5(filename)
-
     def test_to_and_from_pkl_loading(self):
         self.ifo_list.to_pickle(outdir="outdir", label="test")
         filename = "outdir/test_name1name2.pkl"