Dynamic range limitations in signal processing often lead to clipping, or saturation, in signals. The task of audio declipping is estimating the original audio signal, given its clipped measurements, and has attracted much interest in recent years. Audio declipping algorithms often make assumptions about the underlying signal, such as sparsity or low-rankness, and about the measurement system. In this paper, we provide an extensive review of audio declipping algorithms proposed in the literature. For each algorithm, we present assumptions that are made about the audio signal, the modeling domain, and the optimization algorithm. Furthermore, we provide an extensive numerical evaluation of popular declipping algorithms, on real audio data. We evaluate each algorithm in terms of the Signal-to-Distortion Ratio, and also using perceptual metrics of sound quality. The article is accompanied by a repository containing the evaluated methods.