Hierarchical temporal memory (HTM) is a cognitive learning algorithm intended to mimic the working principles of neocortex, part of the human brain said to be responsible for data classification, learning, and making predictions. Based on the combination of various concepts of neuroscience, it has already been shown that the software realization of HTM is effective on different recognition, detection, and prediction making tasks.However, its distinctive features, expressed in terms of hierarchy, modularity, and sparsity, suggest that hardware realization of HTM can be attractive in terms of providing faster processing speed as well as small memory requirements, on-chip area, and total power consumption. Despite there are few works done on hardware realization for HTM, there are promising results which illustrate effectiveness of incorporating an emerging memristor device technology to solve this open-research problem. Hence, this chapter reviews hardware designs for HTM with specific focus on memristive HTM circuits.