Automatic shadow detection is a very important pre-processing step for many remote sensing applications, particularly for images acquired with high spatial resolution. In complex urban environments, shadows may occupy a significant portion of the image. Ignoring these regions would lead to errors in various applications, such as atmospheric correction and classification. To better understand the radiative impact of shadows, a physical study was conducted through the simulation of a synthetic urban canyon scene. Its results helped to explain the most common assumptions made on shadows from a physical point of view in the literature. With this understanding, state-of-the-art methods on shadow detection were surveyed and categorized into six classes: histogram thresholding, invariant color models, object segmentation, geometrical methods, physics-based methods, unsupervised and supervised machine learning methods. Among them, some methods were selected and tested on a large dataset of multispectral and hyperspectral airborne images with high spatial resolution. The dataset chosen contains a large variety of typical occidental urban scenes. The results were compared based on accurate reference shadow masks. In these experiments, histogram thresholding on RGB and NIR channels performed the best with an average accuracy of 92.5%, followed by physics-based methods, such as Richter’s method with 90.0%. Finally, this paper analyzes and discusses the limits of these algorithms, concluding with some recommendations for shadow detection.