Active matter systems consist of self-propelled units that continuously consume energy. This talk presents results on interacting active particle systems, focusing on emergent interactions and active reservoirs. Heterogeneity in the self-propulsion speed of active Brownian particles is shown to generate a pairwise effective short-range repulsion, even when the underlying interaction among the active particles is attractive. This result challenges the common expectation that activity generically induces attraction.
Subsequently, the focus shifts to active reservoirs, a distinct class of nonequilibrium baths. An analytical understanding of tracer dynamics attached to an interacting active bath is developed, followed by an investigation of the nonequilibrium steady state and novel transport properties of a one-dimensional extended system coupled to two active reservoirs with different activities. The talk concludes with some future directions and open questions emerging from these studies.