This 2020 Decadal Survey White Paper reviews what is known about lunar and martian lander Plume Surface Interactions (PSI) during powered descent. This includes an overview of the phenomenology and a description of the induced hardware and environmental impacts. Then it provides an overview of mitigation techniques and a summary of the outstanding questions and strategic knowledge gaps. It finishes with five recommendations: to include dedicated descent imagers on every surface mission so that PSI can be directly recorded and reviewed by ground teams; as far as possible, to make all data related to PSI effects publicly accessible; to develop methods and instruments for making key measurements of PSI; to assess and record key flight data; and to invest funding into studies of long-term infrastructure architectures and mitigation techniques.