The evolution of massive multiple-input multiple-output （MIMO） techniques is an important support for further improving the performance of six-generation （6G） wireless communication systems. However， with the continuous expansion of large-scale antenna arrays， frequency division duplex （FDD） massive MIMO systems are facing severe challenges in acquiring downlink channel state information （CSI）. Deep learning has a powerful ability to learn and process high-dimensional data， which provides a potential solution to this challenge. In this paper， we survey FDD massive MIMO downlink CSI acquisition techniques based on deep learning， including CSI feedback and prediction techniques. Firstly， the theoretical frameworks of CSI feedback and prediction based on deep learning are presented. Then， the superior performance of relevant research results at home and abroad is analyzed， providing a reference scheme for solving the problem of acquiring downlink CSI in FDD massive MIMO systems towards 6G. Finally， unsolved open problems of FDD massive MIMO downlink CSI acquisition are discussed， followed by potential solutions correspondingly.