This work deals with the mechanisms of electronic transitions induced by low-energy positrons. For isolated atomic systems we discuss the role of successive binary collisions, the so-called Thomas mechanisms, between the positron, the excited electron and the atomic core. Furthermore, we consider transfer processes in which one of the charged particles is trapped in a low-lying continuum state of one of the reaction participants. In the second part of the paper, we investigate the various pathways for the secondary-electron emission from metallic surfaces following the bombardment by low-energy positrons. From a formal analysis it is shown that the probability rate for the production of an electron-positron pair is connected to the interacting electron-positron two-particle Green operator. The scattering of the interacting positron-electron subsystem from the crystal potential is treated and it is pointed out that a diffraction of the electron-positron pair as whole might take place leading to characteristic diffraction pattern. The analysis is substantiated by numerical studies for the secondary electron emission from Cu(0 0 1) and Fe(1 1 0) (BCC) samples.