Darwinian natural selection theory has large importance in biology. It has been producing many sub-theories on evolution of animal behavior. Evolutionary psychology is an approach to psychology that employs the evolutionary sub-theories to construct hypotheses on the design of human mind; one of the most interesting biological phenomena. Following an introduction of the natural selection theory, this paper describes some empirical studies on cognitive psychology that have been undertaken with the evolutionary psychological approach. Specifically we will observe the application of a) a theory of social behavior to the study of reasoning, b) a theory of foraging behavior to the study of decision making, and c) sexual selection theory to the study of cognitive sex differences. This paper also presents arguments on domain specificity and innateness of human mind; an important topic that often follows evolutionary psychology. Criticisms on evolutionary psychology will be discussed as well.