  Decaying dark matter models generically modify the equation of state around
the time of dark matter decay, and this in turn modifies the expansion rate of
the Universe through the Friedmann equation. Thus, a priori, these models could
solve or alleviate the Hubble tension, and depending on the lifetime of the
dark matter, they can be classified as belonging to either the early- or
late-time solutions. Moreover, decaying dark matter models can often be
realized in particle physics models relatively easily. However, the
implementations of these models in Einstein--Boltzmann solver codes are
non-trivial, so not all incarnations have been tested. It is well known that
models with very late decay of dark matter do not alleviate the Hubble tension,
and in fact, cosmological data puts severe constraints on the lifetime of such
dark matter scenarios. However, models in which a fraction of the dark matter
decays to dark radiation at early times hold the possibility of modifying the
effective equation of state around matter-radiation equality without affecting
late-time cosmology. This scenario is therefore a simple realization of a
possible early-time solution to the Hubble tension, and cosmological parameter
estimation with current data in these models yields a value of $H_0 =
68.73^{+0.81}_{-1.3}$ at $68\%$ C.I.. This still leads to a $2.7\sigma$
Gaussian tension with the representative local value of $H_0 = 73.2 \pm 1.3$ km
s$^{-1}$ Mpc$^{-1}$. Additional work is, however, required to test more complex
decay scenarios, which could potentially prefer higher values of $H_0$ and
provide a better solution to the Hubble tension.
