In the current information age, the realization of memory devices with energy efficient design, high storage density, nonvolatility, fast access, and low cost is still a great challenge. As a promising technology to meet these stringent requirements, nonvolatile multistates memory (NMSM) has attracted lots of attention over the past years. Owing to the capability to store data in more than a single bit (0 or 1), the storage density is dramatically enhanced without scaling down the memory cell, making memory devices more efficient and less expensive. Multistates in a single cell also provide an unconventional in-memory computing platform beyond the Von Neumann architecture and enable neuromorphic computing with low power consumption. In this review, an in-depth perspective is presented on the recent progress and challenges on the device architectures, material innovation, working mechanisms of various types of NMSMs, including flash, magnetic random-access memory (MRAM), resistive random-access memory (RRAM), ferroelectric random-access memory (FeRAM), and phase-change memory (PCM). The intriguing properties and performance of these NMSMs, which are the key to realizing highly integrated memory hierarchy, are discussed and compared.