A discussion is given of a three-dimensional vortex in a viscous fluid. A theory is outlined that leads to a reduction of the steady-state Navier-Stokes equations of an incompressible fluid to three ordinary, nonlinear, differential equations. Although no numerical results are available, qualitative arguments based on these equations and on the form of their dependent and independent variables throw considerable light on the structure of the vortex. One important result is that the vertical velocity is of the same order of magnitude as the horizontal velocity.