Partial Hyperbolicity introduced about 50 years ago provides a powerful tool for studying high dimensional systems. In the recent year it found powerful applications to chaos theory, rigidity theory, geometry, and number theory. The goal of the conference is to summarize the achievement of partial hyperbolicity theory and discuss open problems. The conference will also include a special session on the history of hyperbolic dynamics. This conference is a part of special program on partial hyperbolicity which will also include the school at the beginning of June.