The computer-vision-based surface defect detection of metal planar materials is a research hotspot in the field of metallurgical industry. The high standard of planar surface quality in the metal manufacturing industry requires that the performance of an automated visual inspection system and its algorithms are constantly improved. This paper attempts to present a comprehensive survey on both two-dimensional and three-dimensional surface defect detection technologies based on reviewing over 160 publications for some typical metal planar material products of steel, aluminum, copper plates and strips. According to the algorithm properties as well as the image features, the existing two-dimensional methodologies are categorized into four groups: statistical, spectral, model, and machine learning-based methods. On the basis of three-dimensional data acquisition, the three-dimensional technologies are divided into stereoscopic vision, photometric stereo, laser scanner, and structured light measurement methods. These classical algorithms and emerging methods are introduced, analyzed, and compared in this review. Finally, the remaining challenges and future research trends of visual defect detection are discussed and forecasted at an abstract level.