This contributed volume is based on talks given at the August 2016 summer school "Fluids Under Pressure," held in Prague as part of the "Prague-Sum" series. Written by experts in their respective fields, chapters explore the complex role that pressure plays in physics, mathematical modeling, and fluid flow analysis. Specific topics covered include: - Oceanic and atmospheric dynamics Incompressible flows Viscous compressible flows Wellposedness of the NavierStokes equations Weak solutions to the NavierStokes equations Fluids Under Pressure will be a valuable resource for graduate students and researchers studying fluid flow dynamics.