Most of the biomedical applications of ultrasound are based on the use of focused ultrasound with a high concentration of energy in the focal region and, respectively, with significant contribution of nonlinear phenomena in ultrasonic bioeffects. The main objective of the current paper is to provide a clear understanding of basic phenomena in nonlinear acoustic fields of focused ultrasound, and to derive simplified equations that would enable physicists and engineers to optimize parameters of biomedical devices for particular applications. Special attention is paid to the contribution of acoustic nonlinearity to the second-order quantities, such as radiation pressure and temperature rise in ultrasonic fields in tissues. Based on asymptotic methods recently developed in nonlinear acoustics, analytical solutions of the equations for the radiation force induced in a dissipative medium are considered. The relationships between parameters of acoustic field and characteristics of biological tissues are quantitatively analyzed. Possible roles of nonlinear acoustic phenomena and ultrasound radiation force in various features of interaction of ultrasonic waves with biological media are discussed.