The fast development of synthesis routes and preparation technology of 2D materials has motivated a rapid growth in the micro‐ and nanoelectronic memory devices, which gives rise to the breakthroughs in the semiconductor research area. Hexagon boron nitride (h‐BN) with excellent chemical, mechanical, and optical properties has been proven to have potential in overcoming the scaling limit to nanometer, and even sub‐nanometer lengths to replace the use of thick and stiff blocking dielectrics in two‐terminal or three‐terminal devices. The use of atomically thin h‐BN or h‐BN van der Waals heterostructures (vdWhs) can improve the reliability, capability, and functionality of memory devices. This is an encouraging strategy toward high‐density on‐chip integrated circuits, which has recently earned considerable interest. While the research in h‐BN material properties and characterization is comprehensively verified, specified mechanisms of resistive switching have not been analyzed in‐depth. Moreover, recent concern about novel structure design and expanding applications in electronics, optoelectronics, and spintronics has arisen. In this review, recent progress in h‐BN memories with volatile or nonvolatile properties is presented, expanding the memories to functional applications, and further challenges of the development of h‐BN‐based memories and logic circuits are discussed. Hexagon boron nitride (h‐BN) with excellent chemical, mechanical, and optical properties has the potential to replace the use of thick and stiff blocking dielectrics in two‐terminal or three‐terminal devices. Recent progress in h‐BN memories with volatile or nonvolatile properties is presented, expanding the memories to functional applications, and further challenges in the development of h‐BN‐based memories are discussed.