Suspensions of swimming bacteria in fluids exhibit incredibly rich behavior, from organization on length scales much longer than the individual particle size to mixing flows and negative viscosities. We will discuss the dynamics of hydrodynamically interacting motile and non-motile stress-generating swimmers or particles as they invade a surrounding viscous fluid, modeled by coupled equations for particle motions and viscous fluid flow. Depending on the type of self-propulsion by its constituents, colonies of swimmers can either exhibit a dramatic splay, or instead a cascade of transverse concentration instabilities as the group moves into the bulk. An active slender-body approximation will be introduced and used in a linear stability analysis of concentrated line distributions of particles, matching the results of our full numerical simulations. Along the way we will prove a very surprising "no-flow theorem": particle distributions initially isotropic in orientation lose isotropy immediately but in such a way that results in no fluid flow anywhere and at any time. Speaker(s): Saverio Spagnolie (University of Wisconsin)