This review provides a detailed description of the Gollin test technique based on the recognition of fragmented images. Important stages in the development of this method are considered, too. The attention is paid to a review of our research conducted using the Gollin test to solve various problems in studying the mechanisms of signal extraction from noise, invariant perception, the insight phenomenon, and modeling the functioning of the nervous system. The neurophysiological mechanisms of incomplete image recognition are discussed. Suggestions are made for possible ways of the further development of the technique and its application in fundamental psychophysiology, systems of artificial intelligence, and medicine.