The CrossScale mission will advance our understanding of fundamental plasma processes in collisionless plasmas. It will exploit the excellent natural plasma laboratory provided by the Earth's magnetosphere and the near-Earth solar wind and, in particular, carry out multi-scale studies that will strongly complement plasma studies in ground-based laboratories. Previous studies of collisionless plasmas in space environments across the solar system have shown the ubiquitous nature of suprathermal particles and that these particles exhibit a power-law energy spectrum. In this paper we discuss the great significance of these suprathermal particles for CrossScale studies. We show that the presence of these particles is a natural consequence of the collisionless regime as they can propagate across the heliosphere with little spectral change and are not thermalised by collisions. They are a key indicator of the non-equilibrium nature of collisionless plasmas and an important source of free energy that can drive plasma processes. We discuss how these suprathermal particles influence the overall properties of the plasma. In particular, the energy distribution of particles follows a Kappa, rather than Maxwellian, distribution and thus the plasma does not have a single thermodynamic temperature. We also discuss the importance of the suprathermal tail as a tool to diagnose the processes responsible for particle energisation in collisionless plasmas. Such energisation is a common feature in collisionless plasmas, especially in terms of the primary science targets for CrossScale: reconnection, shocks and turbulence. Finally we also touch on the value of using CrossScale studies to provide ground truth measurements for a number of astrophysical techniques that exploit the effects of energetic electrons in the distant universe. Throughout the paper, we stress that suprathermal (30 keV-1 MeV) measurements are essential to fully characterise particle distributions. We show that such measurements will benefit greatly from the improved spatial and temporal resolution (compared to Cluster) that is proposed for the HEP instrument on CrossScale. (C) 2010 Elsevier Ltd. All rights reserved.