Summary: The prospects of vortex models of the fine scales of isotropic turbulence are surveyed. These begin with the calculation by J. L. Synge and C. C. Lin in 1943 of longitudinal velocity correlations, using an ensemble of Hill spherical vortices, and are followed by the work of A. A. Townsend [Proc. R. Soc. Lond., Ser. A 208, 534-542 (1951; Zbl 0043.19201)] employing Burgers vortices to study dissipation range scales. Finally, we discuss recent developments by the author and Professor D. I. Pullin based on T. S. Lundgren’s [Phys. Fluids 25, 2193-2203 (1982; Zbl 0536.76034)] work on randomly orientated stretched spiral vortex solutions of the Navier-Stokes equations, for the calculation of higher order moments of one-point velocity gradient statistics and longitudinal velocity correlation functions.