In this chapter, a nonlinear modeling framework called the conditional Gaussian nonlinear system (CGNS) is introduced. The CGNS contains a rich class of nonlinear models, where the joint and marginal distributions can both be highly non-Gaussian, but the conditional distributions of certain variables are Gaussian. Conditional Gaussianity allows the use of closed analytic formulae to solve nonlinear data assimilation problems, which significantly facilitates efficient and accurate simulations and rigorous analysis. The chapter starts by showing that many classical nonlinear systems have CGNS structures. Then, a systematic strategy is presented that approximates general nonlinear models by the CGNS with explicit physical justifications. The analytically solvable conditional statistics of the CGNS advances the study of nonlinear Lagrangian data assimilation. In particular, information theory is combined with the closed analytic formulae of conditional statistics to quantify the uncertainty reduction in recovering turbulent ocean fields by observing multiple tracer trajectories. Furthermore, the CGNS facilitates the development of fast algorithms to solve high-dimensional Fokker-Planck equations that accelerate the ensemble forecast and the calculation of the model response. Real-world examples are utilized to illustrate the entire modeling, data assimilation, ensemble prediction, and uncertainty quantification procedure within the CGNS framework.