  Heusler alloys have been intensively studied due to the wide variety of
properties that they exhibit. One of these properties is of particular interest
for technological applications, i.e. the fact that some Heusler alloys are
half-metallic. In the following, a systematic study of the magnetic properties
of three different Heusler families $\textrm{Co}_2\textrm{Mn}\textrm{Z}$,
$\text{Co}_2\text{Fe}\text{Z}$ and $\textrm{Mn}_2\textrm{V}\textrm{Z}$ with
$\text{Z}=\left(\text{Al, Si, Ga, Ge}\right)$ is performed. A key aspect is the
determination of the Gilbert damping from first principles calculations, with
special focus on the role played by different approximations, the effect that
substitutional disorder and temperature effects. Heisenberg exchange
interactions and critical temperature for the alloys are also calculated as
well as magnon dispersion relations for representative systems, the
ferromagnetic $\textrm{Co}_2\textrm{Fe}\textrm{Si}$ and the ferrimagnetic
$\textrm{Mn}_2\textrm{V}\textrm{Al}$. Correlations effects beyond standard
density-functional theory are treated using both the local spin density
approximation including the Hubbard $U$ and the local spin density
approximation plus dynamical mean field theory approximation, which allows to
determine if dynamical self-energy corrections can remedy some of the
inconsistencies which were previously reported for these alloys.
