Object detection has been vigorously studied for years but fast accurate detection for real-world scenes remains a very challenging problem. Overcoming drawbacks of single-stage detectors, we take aim at precisely detecting objects for static and temporal scenes in real time. Firstly, as a dual refinement mechanism, a novel anchor-offset detection is designed, which includes an anchor refinement, a feature location refinement, and a deformable detection head. This new detection mode is able to simultaneously perform two-step regression and capture accurate object features. Based on the anchor-offset detection, a dual refinement network (DRN) is developed for high-performance static detection, where a multi-deformable head is further designed to leverage contextual information for describing objects. As for temporal detection in videos, temporal refinement networks (TRN) and temporal dual refinement networks (TDRN) are developed by propagating the refinement information across time. We also propose a soft refinement strategy to temporally match object motion with the previous refinement. Our proposed methods are evaluated on PASCAL VOC, COCO, and ImageNet VID datasets. Extensive comparisons on static and temporal detection verify the superiority of DRN, TRN, and TDRN. Consequently, our developed approaches run in a fairly fast speed, and in the meantime achieve a significantly enhanced detection accuracy, i.e., 84.4% mAP on VOC 2007, 83.6% mAP on VOC 2012, 69.4% mAP on VID 2017, and 42.4% AP on COCO. Ultimately, producing encouraging results, our methods are applied to online underwater object detection and grasping with an autonomous system. Codes are publicly available at https://github.com/SeanChenxy/TDRN.