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A review discusses current status of boiling heat transfer research. Basic experimental facts, physical models and correlations of experimental data on heat transfer coefficient (HTC) are reconsidered. Principal restrictions of traditional model of “the theatre of actors” (MTA) are demonstrated. Basic role of control of HTC by thermodynamic conditions on nucleation sites is demonstrated and consequent model of “the theatre of director” (MTD) is discussed. Universal MTD-based correlation of boiling HTC of all types of liquids is presented. Unified consistent research framework for developed boiling heat transfer and diverse specific boiling heat transfer regimes is outlined through supplementing MTD by so-called multifactoring concept (MFC). MFC links transition from developed boiling mode to diverse boiling curves to a phenomenon of multiplication of factors influencing HTC. Multifactoring phenomenon equally can cover any boiling process including boiling in minichannels and microchannels. Possible types of multifactoring are considered. Finally, the ways of further research of the boiling problem are discussed.