The study of jökulhlaups has advanced from describing them qualitatively to measuring systematically on site their discharge curves and source geometry, as well as investigating conditions when particular floods were initiated. In the early days of this science, hypotheses were formulated which attempted to explain the processes responsible for unstable flood growth. The general theory of time-dependent turbulent water flow through intraglacial conduits marked a breakthrough in understanding jökulhlaup hydraulics and has since remained a classical foundation for jökulhlaup studies. This theory described flood evolution in terms of water input into the upper end of a tunnel leading from a reservoir, taking account of sensible stored lake heat and geometry. Such a tunnel expands by positive feedback, since its ice walls melt through frictional heat produced by the flowing water. While this model successfully described jökulhlaups in which the discharge hydrograph increases more or less exponentially over time, other floods were observed which are in stark contrast. In them, pressurized floodwater propagates in a turbulent subglacial water sheet which opens and expands a system of conduits, with an extremely rapid linear rise in discharge. The rushing water enlarges its subglacial pathway not only by melting the ice around it but also by lifting, deforming and fracturing it. Subsequent drainage is nourished by two different sources, with conduit growth being controlled not only by water input at the upper end of the flood path but also by further water joining in, all the way to the edge of the glacier. Moreover, the trigger for releasing meltwater from glacial lakes has been seen to be either of two conduit opening mechanisms, which also determine whether a turbulent subglacial water sheet will result or not. On the one hand, drainage may begin by expanding already existing conduits, in which case the pressure remains lower than that of the ice overburden at the dam and the conduits grow slowly. On the other hand, lake levels may rise until flotation of the ice dam, abruptly opening a sufficient gap for water to propagate as a sheet flow. In order to explain which of these two initiation mechanisms will act, further studies are required into the structure of hydrological drainage systems under ice dams and into their linkage with these two mechanisms. Although current theoretical models of jökulhlaup drainage have managed to reproduce the observed discharge patterns, inconsistencies with the observed behaviour of subglacial drainage systems along the flood path demand further exploration of the actual hydraulic and glaciodynamic processes of jökulhlaups.