Galaxy evolution is shaped by cosmic gas inflows, feedback-driven outflows, and local environment, and understanding the complex interplay between these processes is a key challenge in astrophysics. I will present a multifaceted approach---drawing on observational data, analytic models, and cosmological hydrodynamic simulations---to understanding the evolution of star formation and gas flows in galaxies. Cosmic environment plays a critical role: a third of all low-mass galaxies are satellites in groups or clusters, and satellite quenching is the dominant process for building the quiescent (red-sequence) population at low mass. Satellite-specific processes are also critical for understanding dwarf galaxies of the Local Group. I will discuss work on constraining the environmental dependence of star formation in galaxies and the physical mechanisms responsible for quenching. I also will discuss recent work on isolated dwarf galaxies and their host halos, demonstrating that their gas flow at late cosmic times is largely divorced from the cosmic web and instead is governed largely by rotational support and stellar feedback.