Fluid dynamics is a very old field which is at the same time classical physics and pure mathematics. Some of the most important problems on the physical side, including the emergence and persistence of turbulence, are intimately connected to mathematical issues of singularity formation and propagation for the Euler and Navier-Stokes equations. On the mathematical side, there have been recent breakthroughs in understanding exactly these issues for both incompressible and compressible fluids. This workshop aims to bring together both senior and junior researchers in this area to explain recent progress and highlight future directions of promise.