With the advancement of modern technology, array‐valued data are often encountered in application. Such data can exhibit both high dimensionality and complex structures. Traditional methods for sufficient dimension reduction (SDR) are generally inefficient for array‐valued data as they cannot adequately capture the underlying structure. In this article, we discuss recently developed higher‐order approaches to SDR for regressions with matrix‐ or array‐valued predictors, with a special focus on sliced inverse regressions. These methods can reduce an array‐valued predictor's multiple dimensions simultaneously without losing much/any information for prediction and classification. We briefly discuss the implementation procedure for each method. WIREs Comput Stat 2015, 7:249–257. doi: 10.1002/wics.1354This article is categorized under: Algorithms and Computational Methods > Algorithms Data: Types and Structure > Image and Spatial Data Statistical and Graphical Methods of Data Analysis > Multivariate Analysis