The 6G vision of creating authentic digital twin representations of the physical world calls for new sensing solutions to compose multi-layered maps of our environments. Radio sensing using the mobile communication network as a sensor has the potential to become an essential component of the solution. With the evolution of cellular systems to mmWave bands in 5G and potentially sub-THz bands in 6G, small cell deployments will begin to dominate. Large bandwidth systems deployed in small cell configurations provide an unprecedented opportunity to employ the mobile network for sensing. In this paper, we focus on the major design aspects of such a cellular joint communication and sensing (JCAS) system. We present an analysis of the choice of the waveform that points towards choosing the one that is best suited for communication also for radar sensing. We discuss several techniques for efficiently integrating the sensing capability into the JCAS system, some of which are applicable with NR air-interface for evolved 5G systems. Specifically, methods for reducing sensing overhead by appropriate sensing signal design or by configuring separate numerologies for communications and sensing are presented. Sophisticated use of the sensing signals is shown to reduce the signaling overhead by a factor of 2.67 for an exemplary road traffic monitoring use case. We then present a vision for future advanced JCAS systems building upon distributed massive MIMO and discuss various other research challenges for JCAS that need to be addressed in order to pave the way towards natively integrated JCAS in 6G.