With the advent of the Internet of Things and big data, massive data must be rapidly processed and stored within a short timeframe. This imposes stringent requirements on memory hardware implementation in terms of operation speed, energy consumption, and integration density. To fulfill these demands, 2D materials, which are excellent electronic building blocks, provide numerous possibilities for developing advanced memory device arrays with high performance, smart computing architectures, and desirable downscaling. Over the past few years, 2D‐material‐based memory‐device arrays with different working mechanisms, including defects, filaments, charges, ferroelectricity, and spins, have been increasingly developed. These arrays can be used to implement brain‐inspired computing or sensing with extraordinary performance, architectures, and functionalities. Here, recent research into integrated, state‐of‐the‐art memory devices made from 2D materials, as well as their implications for brain‐inspired computing are surveyed. The existing challenges at the array level are discussed, and the scope for future research is presented.