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The phenomenon of electron tunneling has been known since the advent of quantum mechanics, but continues to enrich our understanding of many fields of physics, as well as creating sub-fields on its own. Spin-dependent tunneling in magnetic tunnel junctions (MTJs) has recently aroused enormous interest and has developed in a vigorous field of research. The large tunneling magnetoresistance (TMR) observed in MTJs garnered much attention due to possible applications in non-volatile random access memories and next-generation magnetic field sensors. This led to a number of fundamental questions regarding the phenomenon of spindependent tunneling. In this review article we present an overview of this field of research. We discuss various factors that control the spin polarization and magnetoresistance in magnetic tunnel junctions. Starting from early experiments on spin-dependent tunneling and their interpretation, we consider thereafter recent experiments and models, which highlight the role of the electronic structure of the ferromagnets, the insulating layer and the ferromagnet/insulator interfaces. We also discuss the role of disorder in the barrier and in the ferromagnetic electrodes and their influence on TMR.