Recently, deep learning has greatly promoted the development of SAR ship detection. But the detectors are usually heavy and computation intensive which hinder the usage on the edge. In order to solve this problem, a lot of lightweight networks and acceleration ideas are proposed. In this survey, we review the papers that about real-time SAR ship detection. We firstly introduce the model compression and acceleration methods. They are pruning, quantization, knowledge distillation, low-rank factorization, lightweight networks and model deployment. They are the source of innovation in real-time SAR ship detection. Then we summarize the real-time object detection methods. They are two-stage, single-stage, anchor free, trained from scratch, model compression and acceleration. Researchers in SAR ship detection usually learn from these ideas. We then spend a lot of content on the review of the 70 real-time SAR ship detection papers. The years, datasets, journals, deep learning frameworks, and hardwares are introduced firstly. After that, the 10 public datasets and the evaluation metrics are shown. Then, we survey the 70 papers according to anchor free, trained from scratch, YOLO series, CFAR+CNN, lightweight backbone, pruning, quantization, knowledge distillation and hardware deployment. The experimental results show that the algorithms have been greatly developed in speed and accuracy. In the end we pointed out the problems of the 70 papers and the directions to be studied in the future. Our work can enable researchers to quickly understand the research status in this field.