The cessation of star-formation in galaxies remains a poorly understood process, despite being one of the most influential events in the evolution of galaxies. It is now known that high stellar density, or compactness, is strongly associated with this process, although the nature of this association is also poorly understood. I will review recent progress on understanding compact and quenched galaxies at high-redshift, and present new results that help constrain the reason for the association between compactness and quenching. Understanding the early evolutionary development of these first quenched galaxies is a major science goal of the James Webb Space Telescope, which will launch in October 2018. I will provide an overview of the observatory capabilities, and discuss how future surveys with this facility will resolve outstanding questions about the nature of quenched galaxies. Finally, I will describe the plans for the Guaranteed Time Observations with this new groundbreaking facility.