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 physical mechanisms by which star formation is suppressed (or “quenched”) in satellite galaxies. In an effort to address this shortcoming, I will present recent work to measure the efficiency of satellite quenching at late cosmic times spanning more than 7 orders of magnitude in satellite stellar mass. In particular, our work utilizes observations of galaxy groups identified in the Sloan Digital Sky Survey as well as detailed studies of dwarfs in the Local Volume to constrain the timescale upon which satellite quenching occurs following infall (and thus the physical mechanisms at play). By bringing together multiwavelength data across a broad range in satellite and host mass, our analysis has established a coherent physical picture of satellite quenching that addresses the most glaring deficiency of current galaxy formation models.