  In this paper, we give a brief survey of recent results on axially symmetric
Navier-Stokes equations (ASNS) in the following categories: regularity
criterion, Liouville property for ancient solutions, decay and vanishing of
stationary solutions. Some discussions also touch on the full 3 dimensional
equations. Two results, closing of the scaling gap for ASNS and vanishing of
homogeneous D solutions in 3 dimensional slabs will be described in more
detail. In the addendum, two new results in the 3rd category will also be
presented, which are generalizations of recently published results by the
author and coauthors.
