•Crystallisation effects on the slag phase assemblage/slag viscosity are reviewed.•Newtonian/non-Newtonian flow transitions in crystallising slags are discussed.•Discrepancy in Tcv definitions is demonstrated; Tcv physical meaning is discussed.•An alternative and more plausible definition of Tcv is suggested and illustrated.•The differences between the characteristic temperatures of slags are demonstrated. The crystallisation in coal ash slags plays a critical role in coal combustion and gasification. The stable operation of a boiler or entrained-flow gasifier is vitally dependent on the easy, continuous removal of combustion by-products in the form of coal ash slags. Of the factors that govern the flow of a coal ash slag in a reactor, slag viscosity is the most important. Crystallisation affects overall slag behaviour and properties, but its most pronounced effect is on slag flow characteristics. It increases slag viscosity, causes Newtonian slag flow to transition to non-Newtonian, and yields the temperature of critical viscosity. In this paper, we systematically review and analyse the complex effect of crystallisation on these three factors.