With advancements in information technology, an enormous amount of data is being generated that must be quickly accessible. However, conventional Si memory cells are approaching their physical limits and will be unable to meet the requirements of intense applications in the future. Notably, 2D atomically thin materials have demonstrated multiple novel physical and chemical properties that can be used to investigate next-generation electronic devices and breakthrough physical limits to continue Moore's Law. Band structure is an important semiconductor parameter that determines their electrical and optical properties. In particular, 2D materials have highly tunable bandgaps and Fermi levels that can be achieved through band structure engineering methods such as heterostructure, substrate engineering, chemical doping, intercalation, and electrostatic doping. In particular, dynamic control of band structure engineering can be used in recent advancements in 2D devices to realize nonvolatile storage performance. This study examines recent advancements in 2D memory devices that utilize band structure engineering. The operational mechanisms and memory characteristics are described for each band structure engineering method. Band structure engineering provides a platform for developing new structures and realizing superior performance with respect to nonvolatile memory.