Nonlinear filtering is a subfield within estimation theory and signal processing concerned with inferring the state of a dynamic system or properties of a signal from noisy measurements. It specifically develops and analyzes methods for systems where the state evolution or observation process involves nonlinear functions, which preclude the direct application of linear filtering techniques. This research area investigates algorithms capable of handling the complex, often non-Gaussian, probability distributions of system states and noise, providing essential tools for accurate estimation and control in diverse applications across engineering, statistics, and applied science where nonlinear dynamics are prevalent.