Large numbers of self propelled units are present in nature from microscopic to macroscopic length scales. Examples are microtubules driven by molecular motors, active colloidal particles, swimming or crawling bacteria, ants, schools of fish, flocks of birds, herds of mammals or robots.
Although interactions between different entities are usually restricted to finite length scales, large scale collective phenomena are often observed.
Because many of the above examples are incredibly complex units, it is desirable to use simplified models to study the major aspects of collective motion. Such models usually share one or more of the following properties that distinguish them from classical statistical mechanics:
1) They are inherently far from thermal equilibrium.
2) They break detailed balance - movies look differently when played forwards or backwards.
3) Galilean invariance is broken.
4) Newtons third law does not apply to the effective interaction rules.
We will discuss, in the context of some widely used models, how kinetic theories and agent-based simulations can be employed in order to gain some level of understanding of the fascinating collective phenomena of self-propelled particles.