Data Assimilation (DA) is the core of modern Numerical Weather Prediction (NWP) systems. However, traditional methods are constrained by bottlenecks such as non-linear and non-Gaussian assumptions as well as high computational cost. Deep Learning (DL), with its powerful non-linear fitting and end-to-end optimization capabilities, offers a revolutionary paradigm to address these challenges. Therefore, from a computer science perspective, this paper reviewed systematically and analyzed a three-stage evolutionary trajectory for the application of DL in meteorological DA: component replacement, paradigm shift, and system reconfiguration. First, it elaborated on the component replacement stage, in which DL serves as surrogate models to replace observation operators and correct model errors, thereby addressing traditional bottlenecks. Second, it provided an in-depth analysis of the paradigm shift stage, where generative models, represented by Variational Auto Encoders (VAEs) and diffusion models, reconstruct the assimilation problem as a probabilistic generation task. Third, it discussed the system reconfiguration stage, in which Artificial Intelligence (AI) meteorological foundation models such as FengWu and FuXi were adopted, and the assimilation module was embedded deeply, so as to construct a closed-loop system of integrated assimilation-forecast. Finally, the paper explored the core challenges in this field, including physical consistency, data dependency, and operational deployment, and prospected future research directions, such as neuro-symbolic fusion and open benchmark construction.