A Vlasov-Maxwell description of the ubiquitous solar coronal structures is presented. It is found that an equilibrium plasma configuration can live with spatial gradients in density, temperature, current and drift speeds of the charged particles. Any stability study must be carried over this inhomogeneous equilibrium state. In addition, the Vlasov description admits the investigation of kinetic processes like heating and radiation and unlike a fluid description, it does not require an equation of state to determine the individual variations of temperature and density