Knots and Links in Fluid Mechanics

In this paper we will review some questions of current interest in fluid mechanics, addressing various geometric aspects of the vortex lines of the fluid. We wil focus on the study of knotted and linked vortex lines, a topic that can be traced back to Lord Kelvin and that was strongly promoted by Arnold and Moffatt in the 1960s. In this context, we will provide a leisurely introduction to some new results on the realization problem for linked vortex lines and vortex tubes of arbitrarily complicated topology.