Axially symmetric Navier-Stokes equations is a special case of the full three dimensional equation describing the motion of viscose impressible fluid. However the lack of understanding is almost the same as the full version case. We will describe results from three groups of people on critical regularity conditions which rule out type I singularity (turbulence). Then we will present a recent joint work with Zhen Lei and Adam Navas. It gives a priori point-wise upper bound on the velocity field, which caps the worst possible singularity.