Smart systems, in which sophisticated software/hardware is embedded in physical systems, are part of everyday life. From simple products with embedded decision-making software, to massive systems in which hundreds of systems, each with hundreds or thousands of embedded processors, interoperate the use of Cyber-Physical Systems (CPS) will continue to expand. There has been substantial investment in CPS research in Europe and the United States. Through a series of workshops and other events, the TAMS4CPS project has established that there is mutual benefit in the European Union and US collaborating on CPS research. An agenda for collaborative research into modelling and simulation for CPS is thus set forth in the publication at hand. The agenda includes models for many different purposes, including fundamental concepts, design models (e.g. architectures), predictive techniques, real-time control, human-CPS interaction, and CPS governance. Within this framework, seven important themes have been identified where mutual benefits can be realised by EU-US cooperation. To actively advance research and innovation in these fields, a number of collaboration mechanisms is presented and concrete actions to encourage, enhance and implement trans-Atlantic collaboration in modelling and simulation of CPS are recommended.