Poincaré coined the term that even completely deterministic dynamical systems show often unpredictable behavior. This phenomenon will be explained (and made precise) using probability theory once a stationary finite measure for the dynamics has been fixed. The talk will discuss some highlights of probabilistic dynamics over the past twenty years, like the validity of central limit theorems, local limit theorems and large deviation. Conversely, probabilistic results for dynamical systems also have some impact to their original dynamics, like for Poincaré exponents of Fuchsian groups, for expressions of the Hausdorff dimension, and ergodicity properties of skew product transformations. If time permits the talk will also discuss the connection of probabilistic dynamics with the original scope of probability theory.