The booming development of artificial intelligence (AI) requires faster physical processing units as well as more efficient algorithms. Recently, reservoir computing (RC) has emerged as an alternative brain‐inspired framework for fast learning with low training cost, since only the weights associated with the output layers should be trained. Physical RC becomes one of the leading paradigms for computation using high‐dimensional, nonlinear, dynamic substrates. Among them, memristor appears to be a simple, adaptable, and efficient framework for constructing physical RC since they exhibit nonlinear features and memory behavior, while memristor‐implemented artificial neural networks display increasing popularity towards neuromorphic computing. In this review, the memristor‐implemented RC systems from the following aspects: architectures, materials, and applications are summarized. It starts with an introduction to the RC structures that can be simulated with memristor blocks. Specific interest then focuses on the dynamic memory behaviors of memristors based on various material systems, optimizing the understanding of the relationship between the relaxation behaviors and materials, which provides guidance and references for building RC systems coped with on‐demand application scenarios. Furthermore, recent advances in the application of memristor‐based physical RC systems are surveyed. In the end, the further prospects of memristor‐implemented RC system in a material view are envisaged.