  We introduce four, a priori different, notions of topological pressure for
possibly discontinuous semiflows acting on compact metric spaces and observe
that they all agree with the classical one when restricted to the continuous
setting. Moreover, for a class of \emph{impulsive semiflows}, which are
examples of discontinuous systems, we prove a variational principle. As a
consequence, we conclude that for this class of systems the four notions
coincide and, moreover, they also coincide with the notion of topological
pressure introduced in \cite{ACS17}.
