Protein remote homology detection is one of the most fundamental and central problems for the studies of protein structures and functions, aiming to detect the distantly evolutionary relationships among proteins via computational methods. During the past decades, many computational approaches have been proposed to solve this important task. These methods have made a substantial contribution to protein remote homology detection. Therefore, it is necessary to give a comprehensive review and comparison on these computational methods. In this article, we divide these computational approaches into three categories, including alignment methods, discriminative methods and ranking methods. Their advantages and disadvantages are discussed in a comprehensive perspective, and their performance is compared on widely used benchmark data sets. Finally, some open questions in this field are further explored and discussed.