The study of the Ornstein-Zernike decay of subcritical two-point functions in equilibrium statistical mechanics has a history going back over a century. Despite this, the crossover from Ornstein-Zernike decay to critical power-law decay has received scant attention in the literature. This talk presents a recent work in which we obtained uniform asymptotics for the subcritical two-point function of random walk (in any d), self-avoiding walk (d >= 5), and percolation (d >= 15). In particular, we established the crossover behaviour on the scale of the correlation length for these models. The proof is based on a general theorem which identifies the asymptotic behaviour of the solution to a convolution equation, and a variational characterisation of the direction-dependent rate of exponential decay. This is joint work with Gordon Slade (University of British Columbia).