In this talk, we present the general principles of binary evolution and give two examples. The first example is the formation of subdwarf B stars (sdBs) and their application to the long-standing problem of ultraviolet excess (also known as UV-upturn) in elliptical galaxies. The second is for the progenitors of type Ia supernovae (SNe Ia). We discuss the main binary interactions, i.e., stable Roche lobe overflow (RLOF) and common envelope (CE) evolution, and show evolutionary channels leading to the formation of various binary-related objects. In the first example, we show that the binary model of sdB stars of Han et al. (2002, 2003) can reproduce field sdB stars and their counterparts, extreme horizontal branch (EHB) stars, in globular clusters. By applying the binary model to the study of evolutionary population synthesis, we have obtained an “a priori” model for the UV-upturn of elliptical galaxies and showed that the UV-upturn is most likely resulted from binary interactions. This has major implications for understanding the evolution of the UV excess and elliptical galaxies in general. In the second example, we introduce the single degenerate channel and the double degenerate channel for the progenitors of SNe Ia. We give the birth rates and delay time distributions for each channel and the distributions of companion stars at the moment of SN explosion for the single degenerate channel, which would help to search for the remnant companion stars observationally.