  In this paper the spectral and scattering properties of a family of
self-adjoint Dirac operators in $L^2(\Omega; \mathbb{C}^4)$, where $\Omega
\subset \mathbb{R}^3$ is either a bounded or an unbounded domain with a compact
$C^2$-smooth boundary, are studied in a systematic way. These operators can be
viewed as the natural relativistic counterpart of Laplacians with Robin
boundary conditions. Among the Dirac operators treated here is also the
so-called MIT bag operator, which has been used by physicists and more recently
was discussed in the mathematical literature. Our approach is based on abstract
boundary triple techniques from extension theory of symmetric operators and a
thorough study of certain classes of (boundary) integral operators, that appear
in a Krein-type resolvent formula. The analysis of the perturbation term in
this formula leads to a description of the spectrum and a Birman-Schwinger
principle, a qualitative understanding of the scattering properties in the case
that $\Omega$ is unbounded, and corresponding trace formulas.
