An impulsive semiflow is prescribed by three ingredients: a continuous semiflow on a space $X$ which governs the state of the system between impulses; a set $D \subset X$ where the flow undergoes some abrupt changes, whose duration is, however, negligible in comparison with the time length of the whole process; and an impulsive function $I:D\to X$ which specifies how a jump event happens each time a trajectory of the flow hits $D$, and whose action may be a source of discontinuities on the trajectories. Dynamical systems with impulsive effects appear to be an appropriate mathematical model to describe real phenomena that exhibit sudden changes in their behavior. In this talk we give sufficient conditions for the existence of invariant probability measures for impulsive semiflows and establish a Variational Principle. Joint work with Maria Carvalho and Carlos Vásquez.