Impulsive dynamical systems may be interpreted as suitable mathematical models of real world phenomena that display abrupt changes in their behavior, and are described by three objects: a continuous semiflow on a metric space X; a set D contained in X; where the flow experiments sudden perturbations; and an impulsive function I : D → X; which determines the change on a trajectory each time it collides with the impulsive set D. We consider impulsive semiflows defined on compact metric spaces and give sufficient conditions, both on the semiflows and the potentials, for the existence and uniqueness of equilibrium states. We also generalize the classical notion of topological pressure to our setting of discontinuous semiflows and prove a variational principle. This is a joint work with José Ferreira Alves and Maria de Fátima de Carvalho.