Geometry problem solving, a crucial aspect of mathematical reasoning, is vital across various domains, including education, the assessment of AI's mathematical abilities, and multimodal capability evaluation. The recent surge in deep learning technologies, particularly the emergence of multimodal large language models, has significantly accelerated research in this area. This paper presents a survey of the applications of deep learning in geometry problem solving, including (i) a comprehensive summary of the relevant tasks in geometry problem solving; (ii) a thorough review of related deep learning methods; (iii) a detailed analysis of evaluation metrics and methods; and (iv) a critical discussion of state-of-the-art performance, existing challenges, and promising future directions. Our objective is to offer a comprehensive and practical reference of deep learning for geometry problem solving, thereby fostering further advancements in this field. We maintain a list of relevant papers: https://github.com/majianz/dl4gps.