Fusion reactions combine light elements in the form of plasma – a hot, charged gas made of positive ions and free-moving electrons, with unique properties distinct from solids, liquids or gases. Plasma modelling is at the forefront of high-performance computing. The EU has invested greatly in the preparation of plasma simulation codes for the exascale era. The EU-funded Plasma-PEPSC project aims to maximise the parallel performance and efficiency of four European flagship plasma codes with a large user base: BIT, GENE, PIConGPU and Vlasiator. Advanced simulations on current pre-exascale and future exascale platforms should allow control of plasma-material interfaces, optimise magnetically confined fusion plasmas, design next-generation plasma accelerators and predict space plasma dynamics in Earth’s magnetosphere.