The appearance of electrons or positrons in dense gaseous media produces a whole series of striking phenomena governed by the properties of the states of the light particles in the dense medium. The present review considers these phenomena systematically. The results of measurements of electron mobility and positron annihilation rates in moderately dense gases are discussed. Effects that arise as the density of the gas increases are considered. Self-trapped states become possible at high densities: these are bound states of the light particles with the medium, ``clusters'', ``bubbles'', or mixed-type formations. The fluctuon theory of these states is set forth, along with the results of experiments in which the light particles make transitions to new states. The possible existence of ``orientation clusters'' in gases consisting of polar molecules is investigated. Certain applications of the results to the theory of discharges in dense gases and liquids and to the theory of the weakly ionized nonideal plasma are discussed.