Ubiquitous in the solar wind and heliosphere suprathermal particle (also known as halo) populations are believed to play key roles in space plasma dynamics, but their effects are far to be understood. Suprathermals enhance the high energy tails of the velocity distributions indicating plasma states out of thermal equilibrium and implicitly an excess of free energy expected to stimulate kinetic effects like instabilities, heating fluxes or energy exchange with plasma waves. With typical energy of a few thermal energies of the core populations, suprathermal populations are markedly enhanced during the energetic events like fast winds and coronal mass ejections suggesting a potential implication on space weather and solar-terrestrial connections. Which are the mechanisms originating these particles, and by which physical processes do they influence the solar wind thermodynamics are just a few examples from the multitude of questions expecting answers from our contributors. The generally accepted representation of Kappa distribution functions invoked to describe these populations and their effects in space plasmas allows for different alternatives which are not always realistic and may prevent a correct interpretation. In this session we propose to debate on all these hot topics by covering both alternative theoretical approaches and in-situ particles, waves and turbulence observations.