Rapid growth in data storage and processing driven by training and inference of large-scale artificial intelligence models necessitates development of novel optical non-volatile memory materials and devices, which offer a promising solution for enhancing computational efficiency while reducing energy consumption in neural networks. Phase-change materials (PCM)-based photonic devices exhibit several advantages in big data processing with high clock frequency, large bandwidth, picosecond latency, and high energy efficiency, making it a key enabler for neuromorphic photonic computing. This review focuses on the recent advancements in optoelectronic PCM for neuromorphic computing. These PCM can be classified into several categories based on their crystallization mechanisms. We provide an in-depth discussion of their bonding mechanisms, optical properties, and performance tuning strategies. Additionally, we review the progress on PCM in photonic waveguide devices for multi-bit storage, bio-inspired synaptic behavior, neuromorphic computing, and hybrid photonic-electronic waveguide technologies. Finally, this review outlines the opportunities and challenges for the research on optoelectronic PCM.