Abstract: Nonlinear Fourier analysis is emerging as a powerful framework for describing nonlinear wave evolution and revealing hidden nonlinear components within complex wave fields. Unlike conventional Fourier analysis, which decomposes a wave field into linear harmonic components, the nonlinear Fourier transform provides a means of identifying nonlinear coherent structures and describing their evolution within the framework of integrable systems. This talk presents recent progress in applying nonlinear spectral methods to field observations of deep water waves. Distinct nonlinear spectral signatures are observed from rogue waves with extreme heights. Recent observations of sea states dominated by ensembles of interacting solitons, commonly referred to as soliton gases, will also be discussed. We will demonstrate how these nonlinear wave structures exhibit statistical properties and discuss their possible physical interpretations in real ocean. The talk will also introduce the basic assumptions and interpretation of nonlinear Fourier analysis, discuss its current limitations, and highlight potential directions for future development and application.