Heterogeneous architectures are increasingly common in modern High-Performance Computing (HPC) systems. Achieving high-performance on such heterogeneous systems requires new approaches to application development that are able to achieve the three Ps: Performance, Portability, and Productivity. In this paper, we provide an overview of the state-of-the-art for developing high-performance, portable and productive multi-physics applications with particular focus on the simulation of a plasma fusion reactor. Simulating such a complex system relies on both fluid- and particle-based simulations, and coupling interfaces between these two domains. We also review the current state-of-the-art in reasoning about the performance, portability and productivity of HPC applications. •Outlines approaches to developing high-performance numerical simulations.•Reviews the state-of-the-art in programming languages and parallel programming models.•Summarises high- and low-level domain specific languages targeting plasma fusion.•Outlines methods for coupling scientific simulations.•Describes methods for reasoning about performance, portability and productivity in HPC.