  Partial hyperbolicity appeared in the sixties as a natural generaliza- tion
of hyperbolicity. In the last 20 years in this area there has been great
activity. Here we survey the state of the art in some topics, focusing
especially in partial hyperbolicity in dimension 3. The reason for this is not
only that it is the smallest dimension in which non-degenerate partial
hyperbolicity can occur, but also that the topology of 3-manifolds influences
this dynamics in revealing ways.
