Summarized in this review are a large number of experimental and modelling studies for advancing the heat-transfer-based mechanism for solid deposition from "waxy" or paraffinic oils and mixtures. This comprehensive heat-transfer approach is entirely different from a more popular molecular-diffusion mechanism. It has evolved from numerous publications, over three decades, which explored topics related to thermodynamic, rheological, crystallization, solid deposition, and shutdown and deposit-aging behaviour of prepared multicomponent paraffinic mixtures of varying compositions to simulate "waxy" crude oils. These investigations covered a wide range of compositions, temperatures, and cooling rates-under static, sheared, laminar and turbulent conditions-in both the hot and cold flow regimes. The heat-transfer mechanism for wax deposition is based on (partial) freezing or liquid-to-solid phase transformation process, for which steady-state and unsteady-state mathematical models have been developed and validated with extensive laboratory data. Furthermore, a shear-induced deformation model for the deposit aging phenomenon has been developed and validated; it is based on a partial release of the liquid phase from the incipient gel, thereby causing an enrichment of heavier alkanes and a corresponding depletion of lighter alkanes in the deposit. A successful analogy with the ice deposition process has confirmed the wax deposition process to be also controlled by heat transfer, without involving any other mechanism for wax deposition. All of these previous studies confirm that wax deposition is predominantly a thermally driven process.