Collections of self-propelled entities, from living cells to engineered microswimmers, organize in a rich variety of active fluid and solid states, with unusual properties. For instance, active fluids can flow with no externally applied driving forces and active gases do not fill their container. In this talk I will describe the behavior of such “active materials” and highlight two examples of active phase transitions. The first is the formation of cohesive matter with no cohesive forces in collections of purely repulsive active colloids. The second is a new density-independent solid-liquid transition in epithelial tissues controlled by cell motility and a cell-shape parameter measuring the interplay ofcortical tension and cell-cell adhesion. An important insight of this work is that cell shape correlates with the mechanical properties of living tissues.