This volume contains the proceedings of the International Conference on Vorticity, Rotation and Symmetry (IV)--Complex Fluids and the Issue of Regularity, held from May 8-12, 2017, in Luminy, Marseille, France. The papers cover topics in mathematical fluid mechanics ranging from the classical regularity issue for solutions of the 3D Navier-Stokes system to compressible and non-Newtonian fluids, MHD flows and mixtures of fluids; discussing topics of different kinds of solutions, boundary conditions, and interfaces.