We review recent evidence showing that cell and tissue dynamics are governed by mesoscale physical principles. These principles can be understood in terms of simple state diagrams in which control variables include force, density, shape, adhesion and self-propulsion. An appropriate combination of these physical quantities gives rise to emergent phenomena such as cell jamming, topological defects and underdamped waves. Mesoscale physical properties of cell assemblies are found to precede and instruct biological functions such as cell division, extrusion, invasion and gradient sensing. These properties are related to properties of biomolecules, but cannot be predicted from biochemical principles. Thus, biological function is governed by emergent mesoscale states that can be predicted by a simple set of physical properties.