Type Ia supernovae (SNe Ia) play a prominent role in understanding the evolution of the Universe. They are thought to be thermonuclear explosions of mass-accreting carbon-oxygen white dwarfs (CO WDs) in binaries, although the mass donors of the accreting WDs are still not well determined. In this article, I review recent studies on mass-accreting WDs, including H- and He-accreting WDs. I also review currently most studied progenitor models of SNe Ia, i.e., the single-degenerate model (including the WD+MS channel, the WD+RG channel and the WD+He star channel), the double-degenerate model (including the violent merger scenario) and the sub-Chandrasekhar mass model. Recent progress on these progenitor models is discussed, including the initial parameter space for producing SNe Ia, the binary evolutionary paths to SNe Ia, the progenitor candidates for SNe Ia, the possible surviving companion stars of SNe Ia, some observational constraints, etc. Some other potential progenitor models of SNe Ia are also summarized, including the hybrid CONe WD model, the core-degenerate model, the double WD collision model, the spin-up/spin-down model and the model of WDs near black holes. To date, it seems that two or more progenitor models are needed to explain the observed diversity among SNe Ia.