The present thesis is devoted to the spectral analysis of transmission and boundary value problems for Dirac operators. Dirac operators are one of the main mathematical tools in relativistic quantum mechanics to describe the propagation of spin 1/2 particles taking relativistic effects into account. In the first part of the thesis Dirac operators with singular delta-shell interactions which are combinations of electrostatic and Lorentz scalar potentials are studied. Such operators are associated to transmission problems for the Dirac equation. The second part of the thesis is then devoted to self-adjoint Dirac operators in domains. With the aid of boundary triples the self-adjointness of the corresponding operators is shown
and some of the spectral data are computed. An interesting property is the existence of critical interaction strengths and boundary values, respectively, for which the associated operators have significantly different spectral properties. Eventually, for Dirac operators with singular interactions also the nonrelativistic limit is computed.