The presentation is to give an outlook about the approaches and results of the creativity research of the past fifteen years, emphasizing the importance of the functional properties of the brain hemispheres in the creative process. A connection is proposed between the recently verified default brain network and the thinking process. On the basis of self-report data examples are given on what we are doing in rest when we seemingly do nothing. The recent data from cognitive neuroscience make it possible to show where this happens in the brain, too. The perceptual style, the psychosexual identification seemingly also determine the creative production. And finally, results of a REM sleep study which demonstrated that the hints exposed before a nap including REM phase are utilized during the creative problemsolving are discussed.