This paper discusses different aspects of bifurcations of periodic solutions in discontinuous systems. It is explained how jumps in the fundamental solution matrix leadto jumps of the Floquet multipliers of periodic solutions. A Floquet multiplier of a discontinuous system can jump through the unit circle causing a discontinuousbifurcation. Numerical examples show discontinuous fold and symmetry-breaking bifurcations. The discontinuous fold bifurcation can connect stable branches tobranches with infinitely unstable periodic solutions.