Intrinsically disordered proteins and regions are widely distributed in proteins, which are associated with many biological processes and diseases. Accurate prediction of intrinsically disordered proteins and regions is critical for both basic research (such as protein structure and function prediction) and practical applications (such as drug development). During the past decades, many computational approaches have been proposed, which have greatly facilitated the development of this important field. Therefore, a comprehensive and updated review is highly required. In this regard, we give a review on the computational methods for intrinsically disordered protein and region prediction, especially focusing on the recent development in this field. These computational approaches are divided into four categories based on their methodologies, including physicochemical-based method, machine-learning-based method, template-based method and meta method. Furthermore, their advantages and disadvantages are also discussed. The performance of 40 state-of-the-art predictors is directly compared on the target proteins in the task of disordered region prediction in the 10th Critical Assessment of protein Structure Prediction. A more comprehensive performance comparison of 45 different predictors is conducted based on seven widely used benchmark data sets. Finally, some open problems and perspectives are discussed.