The problem of automatic geophysical facies classification from well logs has played a crucial role in the mining industry from the 1980s to the present day. During this period, many different approaches were proposed to cope with this task; they were based on the methods of machine learning and deep learning. This paper gives a systematic survey of modern effective solutions to the assigned problem. The comparison of the approaches to the solution which are described in the works of various researchers is presented. The analysis of the available results is given. In addition, this paper provides a detailed description of the set of qualitative input well log data suitable for research.