One of the main purposes of dynamical systems is to understand the behavior of the space of orbits of maps and flows on compact metric spaces. It is often the case that we refer to chaotic dynamical systems whenever it presents dense regular behavior (e.g. periodic) and sensitivity to initial conditions.

In this talk I will discuss several notions of chaoticity in dynamics and  show that typical continuous flows are chaotic. Moreover, we describe some topological and ergodic properties of these flows. This gathers results from collaborations with M. Bessa (UBI), T. Bomfim (UFBA) and M. J. Torres (UM).