The GENERIC framework (General Equation for Non-Equilibrium Reversible Irreversible Coupling) [Öttinger, H. C. Beyond equilibrium thermodynamics. John Wiley & Sons, 2005] provides a systematic method to derive thermodynamically consistent evolution equations. It was originally introduced in the context of complex fluids, and has been employed to a plethora of applications in physics and engineering over the last two decades, such as to anisotropic inelastic solids, viscoplastic solids, and thermoelastic dissipative materials. However, the mathematics of this framework is still under developed. In this talk, I will present some research on the variational structure of the GENERIC and discuss its connections to hypocoercivity and large deviations.