The Complex Absorbing Potential (CAP) method is widely used to compute resonances in Physics and Chemistry, both for nonrelativistic and relativistic Hamiltonians. We give an introduction to the method and, in the semiclassical limit $/hbar /to 0$ we consider resonances near the real axis and we establish the CAP method rigorously for the perturbed Dirac operator by proving that individual resonances are perturbed eigenvalues of the nonselfadjoint CAP Hamiltonian, and vice versa. The proofs are based on pseudodifferential operator theory and microlocal analysis.