The unprecedented advancement of artificial intelligence has placed immense demands on computing hardware, but traditional silicon-based semiconductor technologies are approaching their physical and economic limit, prompting the exploration of novel computing paradigms. Memristor offers a promising solution, enabling in-memory analog computation and massive parallelism, which leads to low latency and power consumption. This manuscript reviews the current status of memristor-based machine learning accelerators, highlighting the milestones achieved in developing prototype chips, that not only accelerate neural networks inference but also tackle other machine learning tasks. More importantly, it discusses our opinion on current key challenges that remain in this field, such as device variation, the need for efficient peripheral circuitry, and systematic co-design and optimization. We also share our perspective on potential future directions, some of which address existing challenges while others explore untouched territories. By addressing these challenges through interdisciplinary efforts spanning device engineering, circuit design, and systems architecture, memristor-based accelerators could significantly advance the capabilities of AI hardware, particularly for edge applications where power efficiency is paramount.