The concept of fear (or anxiety) is of great importance in existential philosophy. Existentialists give fear a positive connotation: we need it in order to pull a person out of a thoughtless life. Fear is like fire, it burns everything unimportant and temporary; only in it is true existence revealed. The first to write about this was Søren Kierkegaard (1813-1855), a Danish philosopher and psychologist, the founder of existentialism. Then the topic was continued by other representatives of this trend, in particular, Rollo May (1909-1994), an American philosopher and psychologist, theorist of existential psychology. It examines the main problems of human existence: anxiety and fear, freedom, responsibility and fate, in addition, it gives a historical overview of the development of these ideas in scientific thought.