This talk is about large deviations for solutions to quasilinear SPDEs with small Gaussian noise. We consider a general variational framework for SPDEs. The large deviation principle (LDP) has been successfully proved for such frameworks by means of the so-called weak convergence approach, but rather strong assumptions must be made on the coefficients in the equation or on the Gelfand triple. In our recently obtained large deviation result, we do not require any additional assumption apart from those required for well-posedness of the equation. This leads to numerous applications for which the LDP was not established yet, such as equations on unbounded spatial domains with gradient noise. In particular, the result solves a long-standing open problem concerning 2D Navier-Stokes. Finally, a generalization of the LDP result will be discussed with a new fluid dynamics application. The talk is based on joint work with Mark Veraar and Antonio Agresti.