The cognitive aspects of creativity in the works by foreign authors are reviewed. Some researchers consider creativity to be an independent process, others see it as the result of other cognitive function interaction. Contribution of various processes (imagination, thinking, memory) to creativity as well as the role of insight is very important. Problems of initiating creativity process, its normativity and different levels are discussed. Creativity process depends on the type and level of intelligence, imagination and memory. The problem of creativity product criteria (originality, the contribution to culture, usefulness) is considered.