  Vorticity plays a prominent role in the dynamics of incompressible viscous
flows. In two-dimensional freely decaying turbulence, after a short transient
period, evolution is essentially driven by interactions of viscous vortices,
the archetype of which is the self-similar Lamb-Oseen vortex. In three
dimensions, amplification of vorticity due to stretching can counterbalance
viscous dissipation and produce stable tubular vortices. This phenomenon is
illustrated in a famous model originally proposed by Burgers, where a straight
vortex tube is produced by a linear uniaxial strain field. In real flows vortex
lines are usually not straight, and can even form closed curves, as in the case
of axisymmetric vortex rings which are very common in nature and in laboratory
experiments. The aim of this chapter is to review a few rigorous results
concerning existence and stability of viscous vortices in simple geometries.
