An account is given in this review of the basic experimental results and theoretical concepts concerning the superfluid A and B phases of $^3$He. The A and B phases of $^3$He possess the most complicated order parameters of all presently known ordered materials, resulting in a rich spectrum of properties of these phases: magnetic, acoustic, superfluid, and others. The theoretical description has been carried out on a phenomenological level, establishing the structure of the superfluid phases of $^3$He on the basis of general concepts of Cooper pairing with nonzero angular momentum and the set of experimental data. A separate section is devoted to linear and nonlinear NMR in superfluid $^3$He. NMR experiments and theory have played an important role in understanding the structure of the superfluid phases of $^3$He.