Radars are widely used to obtain echo information for effective prediction, such as precipitation nowcasting. In this paper, recent relevant scientific investigation and practical efforts using Deep Learning (DL) models for weather radar data analysis and pattern recognition have been reviewed; particularly, in the fields of beam blockage correction, radar echo extrapolation, and precipitation nowcast. Compared to traditional approaches, present DL methods depict better performance and convenience but suffer from stability and generalization. In addition to recent achievements, the latest advancements and existing challenges are also presented and discussed in this paper, trying to lead to reasonable potentials and trends in this highly-concerned field.