Critical heat flux (CHF) is arguably the most important design and safety parameter for any heat-flux controlled boiling application. The present two-part study is focused on CHF for pool boiling from flat surfaces. The first part will review different CHF models and associated mechanisms and parametric trends, while the second part will be dedicated to assessment of CHF models and correlations. Aside from Kutateladze's 1948 pioneering CHF formulation, which is based on dimensional analysis, five different CHF mechanisms are prevalent in the literature: bubble interference, hydrodynamic instability, macro layer dryout, hot/dry spot, and interfacial lift-off. Additionally, many modifications to these mechanisms have been proposed to improve predictive accuracy in tackling the parametric influences of pressure, surface size and roughness, surface orientation, and contact angle. Among the five mechanisms, Zuber's hydrodynamic instability theory has received the most attention because of both its mechanistic formulation and theoretical appeal. More recently, the interfacial lift-off mechanism, which is also theoretically based, has received significant experimental validation, and offers the advantage of tackling different surface orientations. Overall, it is shown that, despite the large body of published pool boiling CHF literature, there are major data gaps in the coverage of relevant parameters. This points to a need for more strategically planned future experiments that would also include microphotographic analysis of near-wall interfacial features, in order to validate or dispute proposed CHF mechanisms. (C) 2017 Elsevier Ltd. All rights reserved.