The rapid development of artificial intelligence (AI) facilitates various applications from all areas but also poses great challenges in its hardware implementation in terms of speed and energy because of the explosive growth of data. Optical computing provides a distinctive perspective to address this bottleneck by harnessing the unique properties of photons including broad bandwidth, low latency, and high energy efficiency. In this review, we introduce the latest developments of optical computing for different AI models, including feedforward neural networks, reservoir computing, and spiking neural networks (SNNs). Recent progress in integrated photonic devices, combined with the rise of AI, provides a great opportunity for the renaissance of optical computing in practical applications. This effort requires multidisciplinary efforts from a broad community. This review provides an overview of the state-of-the-art accomplishments in recent years, discusses the availability of current technologies, and points out various remaining challenges in different aspects to push the frontier. We anticipate that the era of large-scale integrated photonics processors will soon arrive for practical AI applications in the form of hybrid optoelectronic frameworks.