The unprecedented progress in artificial intelligence (AI), particularly in deep learning algorithms with ubiquitous internet connected smart devices, has created a high demand for AI computing on the edge devices. This review studied commercially available edge processors, and the processors that are still in industrial research stages. We categorized state-of-the-art edge processors based on the underlying architecture, such as dataflow, neuromorphic, and processing in-memory (PIM) architecture. The processors are analyzed based on their performance, chip area, energy efficiency, and application domains. The supported programming frameworks, model compression, data precision, and the CMOS fabrication process technology are discussed. Currently, most commercial edge processors utilize dataflow architectures. However, emerging non-von Neumann computing architectures have attracted the attention of the industry in recent years. Neuromorphic processors are highly efficient for performing computation with fewer synaptic operations, and several neuromorphic processors offer online training for secured and personalized AI applications. This review found that the PIM processors show significant energy efficiency and consume less power compared to dataflow and neuromorphic processors. A future direction of the industry could be to implement state-of-the-art deep learning algorithms in emerging non-von Neumann computing paradigms for low-power computing on edge devices.