Although proper pain evaluation is mandatory for establishing the appropriate therapy, self-reported pain level assessment has several limitations. Data-driven artificial intelligence (AI) methods can be employed for research on automatic pain assessment (APA). The goal is the development of objective, standardized, and generalizable instruments useful for pain assessment in different clinical contexts. The purpose of this article is to discuss the state of the art of research and perspectives on APA applications in both research and clinical scenarios. Principles of AI functioning will be addressed. For narrative purposes, AI-based methods are grouped into behavioral-based approaches and neurophysiology-based pain detection methods. Since pain is generally accompanied by spontaneous facial behaviors, several approaches for APA are based on image classification and feature extraction. Language features through natural language strategies, body postures, and respiratory-derived elements are other investigated behavioral-based approaches. Neurophysiology-based pain detection is obtained through electroencephalography, electromyography, electrodermal activity, and other biosignals. Recent approaches involve multimode strategies by combining behaviors with neurophysiological findings. Concerning methods, early studies were conducted by machine learning algorithms such as support vector machine, decision tree, and random forest classifiers. More recently, artificial neural networks such as convolutional and recurrent neural network algorithms are implemented, even in combination. Collaboration programs involving clinicians and computer scientists must be aimed at structuring and processing robust datasets that can be used in various settings, from acute to different chronic pain conditions. Finally, it is crucial to apply the concepts of explainability and ethics when examining AI applications for pain research and management.