The outer layer of the sun, the corona, because it is so hot, streams away from the sun at a high speed: the so-called solar wind. It is a plasma or a completely ionized gas made from charged particles, so that magnetic and electric fields are important for its evolution. The solar wind travels faster than any wave (like a sound wave), so it is a supersonic flow. The solar wind is an example of an astrophysical flow that can actually be studied by in-situ sampling. This has given us an incredibly detailed view of the waves and particles that make up the solar wind. The solar wind is turbulent, so that some of the energy flow occurs between the fluctuations in the wind. Energy cascades from long wavelengths to short, and at some stage the wave energy dissipates and heats the particles. This process affects the overall expansion of the wind. It is a key process in astrophysics which is not fully understood. Turbulence in magnetized collisionless plasmas is one of the major challenges of space physics and astrophysics. In a turbulent cascade fluctuations at a large driving scale contain most of the energy, but there is an energy transfer to fluctuations with ever smaller scales. The dissipation of turbulent fluctuations happens at scales, such as the Larmor radius, where particle kinetics dominates behaviour. Standard ideas of viscous fluid damping are inadequate, and what happens depends on fundamental properties of collisionless plasmas such as non-Maxwellian particle distributions (anisotropies, beams), micro-instabilities and wave-particle coupling. This proposal is for a programme of research which applies the tools of kinetic plasma physics and self-consistent plasma simulations to understanding how astrophysical turbulence dissipates at the smallest scales, and how fundamental properties of collisionless plasmas control or react to the evolution of turbulence. Our work will address some fundamental questions: Why does the collisionless solar wind remain hot as it expands? How does turbulent heating operate in a collisionless plasma? Do ions and electron populations behave differently? Our work will be mostly in the context of the solar wind, as the best observed example of an astrophysical flow, but our results will be applicable over environments from the solar corona to the inter-galactic medium. We will use massively parallel computer simulations to study waves, instabilities and turbulence in astrophysical plasmas. We will also study how this turbulence couplles to energetic particles and affects their transport and acceleration. The simulation codes which will be used have been specially developed to use clusters of hundreds of computational nodes, and will follow the workings of billions of simulational particles. The proposed programme fits into the STFC's mission to support basic research and training in Space Science, and to support advancement of knowledge related to advanced plasma simulation technology. It is closely aligned with key science of the ESA Solar Orbiter mission: ``Determine the properties, dynamics and interactions of plasma, fields and particles in the near-Sun heliosphere''.