For the study of motile cells and other self-propelled particles it is often key to extract quantitative features from trajectories of these particles, both to quantify experimental trajectories and to parametrise theoretical models.

Active nematics is one of the most studied situations in active matter physics, both in theory and experiments.

Dense active suspensions, such as those formed by swarming bacteria, constitute a type of active matter that is particularly hard to model.

The emergence of directed transport as a collective behaviour of many microscopic constituents is a ubiquitous problem in the statistical physics of active particles.

Experimental techniques have demonstrated the ability to alter the collective dynamics of active systems with various types of external perturbations.

Some collective states in active matter exhibit topological properties through the formation of vortices and defects. In some living systems, defects have been shown to have important biological functions.

Passive particles form amorphous solids or glasses at high densities. The same is true of active particles that model living matter such as confluent tissues.

The dynamics of the sperm flagellum has been recently studied with particular attention to its fluctuations. It has been found that the precision of the flagellar beating is close to that of an individual dynein motor powering its motion, which in turn is close to the bound dictated by the thermodynamic uncertainty relation.

Collective tissue behaviour is inherently a multiscale phenomenon that is governed by complex biochemical and mechanical processes occurring simultaneously at the molecular, cellular, and tissue scales.

The spatial organisation of proteins into dense condensates, widely attributed to nonequilibrium phase separation, offers a route to recruit or sequester proteins involved in functions at the cellular level.

Typically, the complex environments in which living systems reside are viscoelastic fluids. For example, the extracellular matrix comprises cross-linked, semiflexible polymeric filaments that respond sensitively to even small stresses generated by cells.

Owing to their active nature, interactions between migrating cells can be non-reciprocal. However, the extent to which cells control their collective behaviour through non-reciprocal interactions remains unclear.

Active field theories are widely used to study collective effects in driven systems at all levels of organisation, allowing instabilities to pattern formation to be identified.

While active matter theory has successfully advanced our understanding of the collective dynamics resulting from individual sources of activity, multiple active processes usually act in concert in real biological systems.

Collective cellular activity and self-organisation phenomena arising from non-equilibrium activity are ubiquitous in tissues and cellular aggregates. However, the relationship between individual properties and biological patterns remains unexplored.