This contributed volume is based on talks given at the August 2016 summer school "e;Fluids Under Pressure,"e; held in Prague as part of the "e;Prague-Sum"e; 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 dynamicsIncompressible flowsViscous compressible flowsWell-posedness of the Navier-Stokes equationsWeak solutions to the Navier-Stokes equationsFluids Under Pressure will be a valuable resource for graduate students and researchers studying fluid flow dynamics.