In this talk, we discuss the long-time behavior of 2d water waves. The first part is concerned with the long-time behavior of rotational water waves. We'll discuss how to construct water wave solution that is subject to the Rayleigh-Taylor instability, and the long-time existence with a pair of counter-rotating point vorticity. In the second part, we'll discuss the application of the NLS approximation of the water waves. Two examples will be discussed, the first one is the rigorous justification of the Peregrine soliton in the water waves, and the second one is the proof of the nonlinear modulational instability of the Stokes waves.

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