  When measuring the value of the Hubble parameter, $H_0$, it is necessary to
know the recession velocity free of the effects of peculiar velocities. In this
work, we study different models of peculiar velocity in the local Universe. In
particular, we compare models based on density reconstruction from galaxy
redshift surveys and kernel smoothing of peculiar velocity data. The velocity
field from the density reconstruction is obtained using the 2M++ galaxy
redshift compilation, which is compared to two adaptive kernel-smoothed
velocity fields: the first obtained from the 6dF Fundamental Plane sample and
the other using a Tully-Fisher catalogue obtained by combining SFI++ and 2MTF.
We highlight that smoothed velocity fields should be rescaled to obtain
unbiased velocity estimates. Comparing the predictions of these models to the
observations from a few test sets of peculiar velocity data, obtained from the
Second Amendment Supernovae catalogue and the Tully-Fisher catalogues, we find
that 2M++ reconstruction provides a better model of the peculiar velocity in
the local Universe than the kernel-smoothed peculiar velocity models. We study
the impact of peculiar velocities on the measurement of $H_0$ from
gravitational waves and megamasers. In doing so, we introduce a probabilistic
framework to marginalize over the peculiar velocity corrections along the
line-of-sight. For the megamasers, we find $H_0 = 69^{+2.9}_{-2.8}$ km s^{-1}
Mpc^{-1} using the 2M++ velocity field. We also study the peculiar velocity of
the the galaxy NGC1052-DF2, concluding that a short $\sim$ 13 Mpc distance is
not a likely explanation of the anomalously low dark matter fraction of that
galaxy.
