Recent experiments, theory and modelling of positron interactions with atoms and molecules are discussed. The first half of the paper is devoted to binary collisions between positrons and crossed beams of atoms or molecules (in this case neon) and the second half deals with ensembles of non-interacting positrons, otherwise known as swarms which are transported through the background gas. We review the recent results on measurements of the cross sections based on obtained from collisional positron traps and subsequent calculations of transport properties of positron swarms that may be used to model thermalization experiments, collisional traps and possible applications of positrons in materials science and biomedicine. It was found that kinetic phenomena occur in positron transport that are mainly the result of the positronium (Ps) formation which has a larger cross section than elastic scattering in most gases and at the same time is a non-conservative process. Most importantly negative differential conductivity (NDC) occurs only for the bulk drift velocity while it does not exist for the flux property, a phenomenon that has not been observed for electrons
