Dynamic range limitations in signal processing often lead to clipping, or saturation, in signals. Audio declipping is the task of estimating the original audio signal given its clipped measurements and has attracted a lot of interest in recent years. Audio declipping algorithms often make assumptions about the underlying signal, such as sparsity or low-rankness, as well as the measurement system. In this paper, we provide an extensive review of audio declipping algorithms proposed in the literature. For each algorithm, we present the assumptions being made about the audio signal, the modeling domain, as well as 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, as well as using perceptual metrics of sound quality. The article is accompanied with the repository containing the evaluated methods.