Nonlinear Resonance Analysis (NRA) is a natural next step after Fourier analysis developed for linear PDEs. The main subject of NRA is nonlinear PDEs, possessing resonant solutions. The very special role of resonant solutions has been first demonstrated by Poincare, for nonlinear ODEs, and generalized to nonlinear PDEs in the frame of Kolmogorov-Arnold-Moser-theory (KAM-theory). The importance of NRA is due to its wide application area -- from climate predictability to cancer diagnostic to breaking of the wing of an aircraft. NRA can also be regarded as a necessary preliminary step for numerical simulations with a big number N of eigenmodes in Galerkin-like methods. NRA allows reducing drastically the number of eigen-modes (and, correspondingly, the computation time). Namely, N ~ 10**6 can be reduced to mostly ~10**3, N ~ 10**3 can be reduced to mostly ~10**2, N ~ 10 can be reduced to mostly ~10 (in these cases, analytical solutions can often be constructed and numerical simulations might become superfluous). In this talk I am going to give a brief overview of the methods and results available in NRA, and illustrate it with some examples from fluid mechanics.