Machine learning (ML) offers a variety of techniques to understand many complex problems in different fields. The field of heat transfer, and thermal systems in general, are governed by complicated sets of physics that can be made tractable by reduced-order modeling and by extracting simple trends from measured data. Therefore, ML algorithms can yield computationally efficient models for more accurate predictions or to generate robust optimization frameworks. This study reviews past and present efforts that use ML techniques in heat transfer from the fundamental level to full-scale applications, including the use of ML to build reduced-order models, predict heat transfer coefficients and pressure drop, perform real-time analysis of complex experimental data, and optimize large-scale thermal systems in a variety of applications. The appropriateness of different data-driven ML models in heat transfer problems is discussed. Finally, some of the imminent opportunities and challenges that the heat transfer community faces in this exciting and rapidly growing field are identified.