The grand challenge facing the power and energy industries is the development of efficient, environmentally friendly, and affordable technologies for next-generation energy systems. To provide solutions for energy and the environment, the U.S. Department of Energy's (DOE) National Energy Technology Laboratory (NETL) and its research partners in industry and academia are relying increasingly on the use of sophisticated computer-aided process design and optimization tools. In this paper, we describe recent progress toward developing an Advanced Process Engineering Co-Simulator (APECS) for the high-fidelity design, analysis, and optimization of energy plants. The APECS software system combines steady-state process simulation with multiphysics-based equipment simulations, such as those based on computational fluid dynamics (CFD). These co-simulation capabilities enable design engineers to optimize overall process performance with respect to complex thermal and fluid flow phenomena arising in key plant equipment items, such as combustors, gasifiers, turbines, and carbon capture devices. In this paper we review several applications of the APECS co-simulation technology to advanced energy systems, including coal-fired energy plants with carbon capture. This paper also discusses ongoing co-simulation R&D activities and challenges in areas such as CFD-based reduced-order modeling, knowledge management, advanced analysis and optimization, and virtual plant co-simulation. Continued progress in co-simulation technology - through improved integration, solution, and deployment - will have profound positive impacts on the design and optimization of high-efficiency, near-zero emission fossil energy systems. Published by Elsevier Ltd.