Road extraction from high-resolution remote sensing images (HRSI) is a challenging but hot research topic in the past decades. A large number of methods are invented to deal with this problem. This article provides a comprehensive review of these existing approaches. We classified the methods into heuristic and data-driven. The heuristic methods are the mainstream in the early years, and the data-driven methods based on deep learning have been quickly developed recently. With regard to the heuristic methods, the road feature model is firstly introduced, then, the classic extraction methods are reviewed in two sub-categories: semi-automatic and automatic. The principles, inspirations, advantages and disadvantages of these methods are described. In terms of the data-driven methods, the road extraction methods based on deep neural network, particularly those based on patched convolutional neural network, fully convolutional network and generative adversarial network are reviewed. We perform subjective comparisons between the methods inner each type. Furthermore, the quantity performances achieved on the same dataset are compared between the heuristic and data-driven methods to show the strengthening of the data-driven methods. Finally, the conclusion and prospects are summarized.