This chapter is devoted to the description of fluid flows. First, the barotropic compressible Navier-Stokes system is introduced together with boundary conditions studied in the book, no-slip boundary conditions and Navier slip boundary conditions. The renormalized version of continuity equation is stated, and assumptions on the pressure are given. Weak solutions and finite energy weak solutions to problems with both versions of boundary conditions are defined. Second, the full Navier-Stokes-Fourier system is introduced together with hypothesis on viscosities, heat conductivity and the pressure, internal energy, and entropy. Variational solutions for both versions of boundary conditions for velocity are defined.