The current developments in the research area are marked by a significant shift towards integrating machine learning techniques with traditional methods to enhance the modeling and prediction of complex dynamical systems. There is a notable emphasis on developing frameworks that not only improve the accuracy of predictions but also facilitate efficient data assimilation, a critical aspect for state estimation and model identification. The use of deep learning models, particularly those incorporating conditional Gaussian structures and Koopman theory, is gaining traction for their ability to handle nonlinear dynamics and non-Gaussian features with appropriate uncertainty quantification. Additionally, there is a growing interest in gradient-free training methods for recurrent neural networks, which address the challenges posed by traditional gradient-based training approaches. These advancements are not only improving the computational efficiency and robustness of models but also expanding their applicability to a wider range of complex systems, including those with sparse and random observations. Notably, the integration of ensemble data assimilation with particle-based methods and the development of novel deep learning frameworks for dynamic systems are particularly noteworthy for their innovative approaches and promising results.