This paper reviews the current status of boiling heat transfer modelling, discusses the need for its improvement due to unresolved intriguing experimental findings and emergence of novel technical applications and outlines the directions for an advanced modelling approach. The state-of-the-art of computational boiling heat transfer studies is given for: macro-scale boiling models applied in two-fluid liquid-vapour interpenetrating media approach, micro-, meso-scale boiling computations by interface capturing methods, and nano-scale boiling simulations by molecular dynamics tools. Advantages, limitations and shortcomings of each approach, which originate from its grounding formulations, are discussed and illustrated on results obtained by the boiling model developed in our research group. Based on these issues, we stress the importance of adaptation of a multi-scale approach for development of an advanced boiling predictive methodology. A general road-map is outlined for achieving this challenging goal, which should include: improvement of existing methods for computation of boiling on different scales and development of conceptually new algorithms for linking of individual scale methods. As dramatically different time steps of integration for different boiling scales hinder the application of full multi-scale methodology on boiling problems of practical significance, we emphasise the importance of development of another algorithm for the determination of sub-domains within a macro-scale boiling region, which are relevant for conductance of small-scale simulations.