Recombination of excess nonequilibrium electrons and holes in semiconductors through impurity recombination centers traps known as trap-assisted ShockleyRead-Hall recombination is in many cases the dominant process. In this chapter, we develop the general theory of trap-assisted recombination and study in detail two key characteristics dependences of excess charge carriers' lifetime and photoelectric gain on concentration N of recombination centers and effectiveness of band-toband photoexcitation of charge carriers and photo-emf in semiconductors at low-level illumination considered outside quasi-neutrality approximation.