Safe learning and optimization deals with learning and optimization problems that avoid, as much as possible, the evaluation of non-safe input points, which are solutions, policies, or strategies that cause an irrecoverable loss (e.g., breakage of a machine or equipment, or life threat). Although a comprehensive survey of safe reinforcement learning algorithms was published in 2015, a number of new algorithms have been proposed thereafter, and related works in active learning and in optimization were not considered. This paper reviews those algorithms from a number of domains including reinforcement learning, Gaussian process regression and classification, evolutionary algorithms, and active learning. We provide the fundamental concepts on which the reviewed algorithms are based and a characterization of the individual algorithms. We conclude by explaining how the algorithms are connected and suggestions for future research.