In recent years, the rapid progression of artificial intelligence and the Internet of Things has led to a significant increase in the demand for advanced computing capabilities and more robust data storage solutions. In light of these challenges, neuromorphic computing, inspired by human brain’s architecture and operation principle, has surfaced as a promising answer to the growing technological demands. This novel methodology emulates the biological synaptic mechanisms for information processing, enabling efficient data transmission and computation at the identical position. Two-dimensional (2D) materials, distinguished by their atomic thickness and tunable physical properties, exhibit substantial potential in emulating synaptic plasticity and find broad applications in neuromorphic computing. With respect to device architecture, memory devices based on floating-gate (FG) structures demonstrate robust data retention capabilities and have been widely used in the realm of flash memory. This review begins with a succinct introduction to 2D materials and FG transistors, followed by an in-depth discussion on remarkable research progress in the integration of 2D materials with FG transistors for applications in neuromorphic computing and memory. This paper offers a thorough review of the existing research landscape, encapsulating the notable progress in swiftly expanding field. In conclusion, it addresses the constraints encountered by FG transistors using 2D materials and delineates potential future trajectories for investigation and innovation within this area.