Despite remarkable success at modeling the evolution of massive galaxies over cosmic time, modern hydrodynamic and semi-analytic models of galaxy formation fail to reproduce the properties of low-mass galaxies. This shortcoming in our theoretical picture is  largely driven by an inability to understand the physics of satellite
(or “environmental”) quenching. Using observations of satellite galaxies in the SDSS as well as detailed studies of dwarfs in the Local Volume, I will present recent work to constrain the timescale  on which star formation is suppressed in low-mass satellites, focusing on the potential physical mechanisms that may be at play. As time allows, I’ll also discuss ongoing work to study the spatial anisotropy in satellite distributions as a test of the Lambda-CDM paradigm.