This paper provides a comprehensive review on the application of proppants to maintain fracture permeability over the lifetime of a well based on published observations from experiments and modeling. The review identifies and describes important processes occurring during proppant embedment, during hydraulic fracturing, laboratory testing of fracture conductivity, proppant embedment and modeling of proppant embedment. Finally, this paper identifies the challenges and knowledge gaps that also provide future avenues of research and opportunities for collaborative technological development which requires an interdisciplinary approach of science, engineering in academia, government, and private sector.