Deep learning, in general, focuses on training a neural network from large labeled datasets. Yet, in many cases there is value in training a network just from the input at hand. This is particularly relevant in many signal and image processing problems where training data is scarce and diversity is large on the one hand, and on the other, there is a lot of structure in the data that can be exploited. Using this information is the key to deep internal-learning strategies, which may involve training a network from scratch using a single input or adapting an already trained network to a provided input example at inference time. This survey paper aims at covering deep internal-learning techniques that have been proposed in the past few years for these two important directions. While our main focus will be on image processing problems, most of the approaches that we survey are derived for general signals (vectors with recurring patterns that can be distinguished from noise) and are therefore applicable to other modalities.