  Large-scale collective behavior in suspensions of many particles can be
understood from the balance of statistical forces emerging beyond the direct
microscopic particle interactions. Here we review some aspects of the
collective forces that can arise in suspensions of self-propelled active
Brownian particles: wall forces under confinement, interfacial forces, and
forces on immersed bodies mediated by the suspension. Even for non-aligning
active particles, these forces are intimately related to a non-uniform
polarization of particle orientations induced by walls and bodies, or
inhomogeneous density profiles. We conclude by pointing out future directions
and promising areas for the application of collective forces in synthetic
active matter, as well as their role in living active matter.
