Self-awareness is the ability of a subject to discriminate itself from other subjects and the external world as a whole. Self-awareness is а key component of consciousness, the latter being the highest level of phylogenetic and ontogenetic development of the mind. Traditionally, the technique of self-recognition in the mirror is used to study the preconditions of self-awareness in animals. For a long time, it has been an almost common belief that the ability of self-awareness is closely related to the ability to understand others, and therefore, to the social nature of consciousness. However, recent empirical evidence suggests that this ability may be discovered in the animals with qualitatively different mind and life activities than humans and species that are systematically close to humans. We describe our specific approach to the study of the self-awareness phenomenon. Basing on generalization of a number of data we conclude that any animals take into account the characteristics of their bodies when regulating their behavior. In order to avoid terminological confusion, we use the term self-reflection to denote this phenomenon. The author also highlights the main trends in the evolution of self-reflection.