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The expansion of optoelectronic devices on photonic integration platforms has led to significant growth in the field of photonic computing. Photonic integrated circuits have facilitated the creation of ultrafast artificial neural networks, forming the basis for a novel category of information processing devices. Their application extends to diverse domains such as medical diagnosis, language models, telecommunications, quantum computing, and the metaverse, addressing the escalating demands of machine learning and artificial intelligence (AI). In contrast, conventional electronics faces challenges in latency, crosstalk, and energy consumption. Neuromorphic photonics emerges as a compelling solution, featuring sub-nanosecond latencies, minimal heat dissipation, and high parallelism, expanding the scope of AI and Optical Neural Networks. This review explores recent advances in integrated photonic neuromorphic systems, focusing on materials and device engineering breakthroughs needed to overcome existing challenges. Examining various technologies in AI accelerators, from traditional optics to PICs, we assess energy efficiency through operations per joule and compute density in operations per squared millimeter per second. A comparative analysis highlights crucial technical aspects, emphasizing nanophotonic components like VCSEL lasers, optical interconnects, nanocavity resonators, and frequency microcombs. These components showcase recent breakthroughs in photonic engineering and materials science, enabling the creation of customized neuromorphic systems for AI tasks. Despite progress, current technologies face obstacles in achieving photonic AI accelerators with computing speed and energy efficiencies reaching the petaOPS range. The review explores potential future approaches in new devices, fabrication, materials, scalability, and integration to enhance critical performance metrics., Comment: 39 pages,17 figures