  Learning curves provide insight into the dependence of a learner's
generalization performance on the training set size. This important tool can be
used for model selection, to predict the effect of more training data, and to
reduce the computational complexity of model training and hyperparameter
tuning. This review recounts the origins of the term, provides a formal
definition of the learning curve, and briefly covers basics such as its
estimation. Our main contribution is a comprehensive overview of the literature
regarding the shape of learning curves. We discuss empirical and theoretical
evidence that supports well-behaved curves that often have the shape of a power
law or an exponential. We consider the learning curves of Gaussian processes,
the complex shapes they can display, and the factors influencing them. We draw
specific attention to examples of learning curves that are ill-behaved, showing
worse learning performance with more training data. To wrap up, we point out
various open problems that warrant deeper empirical and theoretical
investigation. All in all, our review underscores that learning curves are
surprisingly diverse and no universal model can be identified.
