As society’s appetite for information continues to grow, so does our need to process this information with increasing speed and versatility. Many believe that the one-size-fits-all solution of digital electronics is becoming a limiting factor in certain areas such as data links, cognitive radio, and ultrafast control. Analog photonic devices have found relatively simple signal processing niches where electronics can no longer provide sufficient speed and reconfigurability. Recently, the landscape for commercially manufacturable photonic chips has been changing rapidly and now promises to achieve economies of scale previously enjoyed solely by microelectronics. By bridging the mathematical prowess of artificial neural networks to the underlying physics of optoelectronic devices, neuromorphic photonics could breach new domains of information processing demanding significant complexity, low cost, and unmatched speed. In this article, we review the progress in neuromorphic photonics, focusing on photonic integrated devices. The challenges and design rules for optoelectronic instantiation of artificial neurons are presented. The proposed photonic architecture revolves around the processing network node composed of two parts: a nonlinear element and a network interface. We then survey excitable lasers in the recent literature as candidates for the nonlinear node and microring-resonator weight banks as the network interface. Finally, we compare metrics between neuromorphic electronics and neuromorphic photonics and discuss potential applications.