Software self-adaptation (SSA) provides a way of dealing with dynamic environment and uncertain requirement. There are existing works that transform the dynamic and uncertainty concerned by SSA into regression, classification, cluster, or decision problems; and apply machine learning algorithms, including reinforcement learning, neural network/deep learning, Bayesian decision theory and probabilistic graphical model, rule learning, to problem formulation and solving. These kinds of work are called as “machine learning enabled SSA” in this study. The survey is conducted on the state-of-the-art research about machine learning enabled SSA by firstly explaining the related concepts of SSA and machine learning; and then proposing a taxonomy based on current work from SSA perspective and machine learning perspective respectively; analyzing the machine learning algorithms, software external interaction, software internal control, adaptation process, the relationship between SSA task and learning ability under this taxonomy; as well as identifying finally deficiency of current work and highlighting future research trends.