Impulsive Dynamical Systems (IDS) can be seen as suitable mathematical models of real world phenomena that display abrupt changes in their behavior.

More precisely, an IDS is described by three objects: a continuous semiflow on a space X; a set D contained in X where the flow undergoes sudden perturbations; and an impulsive function from D to X, which determines the change in the trajectory each time it collides with the impulsive set D.

In spite of their great range of applications, IDS have started being studied from the viewpoint of ergodic theory only quite recently in the work of Alves and Carvalho. A key challenge, inherent to the dynamics, is that in general, an impulsive semiflow is not continuous.

In this talk I will provide sufficient conditions for the existence of invariant measures that imply the ones given by Alves and Carvalho and are somewhat easier to verify. Moreover, I will discuss some ideas on how typical is the invariance of the non-wandering set of an impulsive semiflow. This talk is based upon two works in progress with Afonso and Bonotto and with Torres and Varandas.