A survey of the present state of the theory of rotational Brownian motion is given. Chapters 1 and 2 expound the theory of rotational diffusion and the solution of the problem of rotational random walks. The probability distributions for the orientations of Brownian particles are written in terms of generalized spherical functions, which are matrix elements of irreducible representations of the rotation group. Methods are discussed for the experimental determination of the nature of Brownian rotation by the use of nuclear magnetic resonance, dielectric relaxation, and the Rayleigh scattering of light. Chapter 3 gives an exposition of generalized rotational diffusion, taking account of inertial effects in the Brownian motion. The influence of inertial effects on dielectric magnetic relaxation and on the scattering of light is discussed. The conclusion of the review gives a discussion of precession effects in Brownian motion.