Industry is moving towards advanced Cyber-Physical Systems (CPS), with trends in smartness, automation, connectivity and collaboration. We examine the drivers and requirements for the use of edge computing in critical industrial applications. Our purpose is to provide a better understanding of industrial needs and to initiate a discussion on what role edge computing could take, complementing current industrial and embedded systems, and the cloud. Four domains are chosen for analysis with representative use-cases; manufacturing, transportation, the energy sector and networked applications in the defense domain. We further discuss challenges, open issues and suggested directions that are needed to pave the way for the use of edge computing in industrial CPS.