The term “artificial intelligence (AI)” was coined in 1956, and its development has undergone periods of extreme hype and periods of strong disillusionment since then. Today, AI has received tremendous attention from both academia and industry, and it will remain one of the hottest topics in the foreseeable future. A subset of AI named machine learning (ML) has achieved great success throughout a huge variety of fields, such as computer vision, natural language processing, and computer gaming. ML was first proposed to endow machine the ability to imitate the learning process of the human brain using neuromorphic models. However, the modelling complexity and limited computing capabilities of machines hindered the development of ML in its early days. Benefiting from the ever-growing computing power and availability of digital data, ML has adopted both bio-inspired spiking neural network (SNN), or neuromorphic computing, and practical artificial neural network (ANN), which have become two of the top trending methods with outstanding results. This chapter gives a brief overview of the state-of-the-art architectures and circuits for ML. On the one hand, neuromorphic computing architectures and accelerators are investigated, including bio-inspired computational models and learning methods, microarchitecture, circuit-level design considerations, and prominent neuromorphic chips. On the other hand, architectures for ANNs are outlined, including essential design metrics on ANN accelerators and various state-of-the-art ANN architectures and circuits.