The talk will focus on the asymptotic analysis of fracture propagation driven by a viscous fluid in a linear elastic solid with small toughness. A priori unknown lag between the fluid and fracture fronts will be taken in consideration. Upon discussion of the fluid-driven fracture scaling, it will be shown that two asymptotic regimes exist. The first regime develops when the fracture propagates under large confining stress or, equivalently, at large time. This regime corresponds to a fully fluid-filled crack (nearly zero lag). The other regime characterizes propagation under small (or zero) confining stress or, equivalently, at small time, and corresponds to the fluid-filled fraction of the crack being small (the lag accounts for most of the fracture length. Under conditions of small toughness, both asymptotic cases are singular perturbation problems. In the large stress/time case, the solution on the scale of the fracture is given by the zero-toughness zero-lag solution, whereas the influence of toughness is localized to a tip boundary layer possessing the linear elastic fracture mechanics singularity at the fracture tip. In the small stress/time case, the injected fluid forms a thin boundary layer near the fracture inlet while the solution away from the inlet is provided by the solution for the crack loaded at the center by a pair of concentrated forces. The latter are obtained from the solution of the inlet fluid boundary layer.