  In this survey we gather recent results on Dirac operators coupled with
$\delta$-shell interactions. We start by discussing recent advances regarding
the question of self-adjointness for these operators. Afterward we switch to an
approximation question: can these operators be recovered as limits of Dirac
operators coupled with squeezing potentials ? We also discuss spectral features
of these models. Namely, we recall the main spectral consequences of a
resolvent formula and conclude the survey by commenting a result of asymptotic
nature for the eigenvalues in the gap of a Dirac operator coupled with a
Lorentz-scalar interaction.
