The tools of soft matter, in which mesoscopically large entities are coarse grained into relatively simple degrees of freedom, are being increasingly used to predict the behavior of active and even living systems. Prominent examples include models for bird flocks, or models for the mechanics and rheology of dense cellular matter. Constructing these models typically involves an implicit coarse graining over a highly non-equilibrium set of degrees of freedom, and it is far from apparent that the classical theoretical frameworks that are typically then used are appropriate. This talk will combine large scale numerical simulations of a variety of models --- from models of tissue mechanics to Vicsek-style models of flocks --- to highlight some of these subtleties. I will highlight the novel universality class that seems to characterize the disordered solid state of these “geometric” models of dense cellular matter, and the apparent non-reciprocal interactions present in models of flocking. I will highlight how these effects imply unexpected terms in a hydrodynamic description of these models, leading to predictions of new collective dynamics at large scales.