The pool boiling process is one of the most effective heat transfer modes capable of transferring large amounts of heat with small temperature difference between the heated surface and the fluid. In addition, fundamental knowledge of pool boiling processes is the starting point of flow boiling research and applications. It is therefore no surprise that it has been, and still is, the subject of extensive research globally for quite some time and a critical analysis is now required in order to move forward with enhanced surface designs. The current on-going research focuses on the understanding of boiling fundamentals including bubble generation, growth and bubble dynamics. In this context, fluid-surface interaction is critical. In the first part of this two-part paper we present the factors and parameters affecting the above, starting with the criteria for gas/vapour entrapment, nucleation site stability and the superheat required for heterogeneous nucleation. The models predicting the incipience superheat are critically described, classified into phase instability and superheated boundary-layer based models. This first part includes bubble growth and departure models, elucidating the effect of surface topology and wettability that can inform and facilitate the design of enhanced surfaces that are presented in Part II [10]. Three fluids of industrial interest, i.e. FC-72, HFE7100 and water were used through the discussion, as examples, to represent low and high surface tension fluids and help the understanding of surface-fluid interactions and relation to possible heat transfer enhancements.