In the dynamic landscape of Artificial Intelligence (AI), two notable phenomena are becoming predominant: the exponential growth of large AI model sizes and the explosion of massive amount of data. Meanwhile, scientific research such as quantum computing and protein synthesis increasingly demand higher computing capacities. As the Moore's Law approaches its terminus, there is an urgent need for alternative computing paradigms that satisfy this growing computing demand and break through the barrier of the von Neumann model. Neuromorphic computing, inspired by the mechanism and functionality of human brains, uses physical artificial neurons to do computations and is drawing widespread attention. This review studies the expansion of optoelectronic devices on photonic integration platforms that has led to significant growth in photonic computing, where photonic integrated circuits (PICs) have enabled ultrafast artificial neural networks (ANN) with sub-nanosecond latencies, low heat dissipation, and high parallelism. In particular, various technologies and devices employed in neuromorphic photonic AI accelerators, spanning from traditional optics to PCSEL lasers are examined. Lastly, it is recognized that existing neuromorphic technologies encounter obstacles in meeting the peta-level computing speed and energy efficiency threshold, and potential approaches in new devices, fabrication, materials, and integration to drive innovation are also explored. As the current challenges and barriers in cost, scalability, footprint, and computing capacity are resolved one-by-one, photonic neuromorphic systems are bound to co-exist with, if not replace, conventional electronic computers and transform the landscape of AI and scientific computing in the foreseeablefuture.