Remote sensing object detection (RSOD), one of the most fundamental and challenging tasks in the remote sensing field, has received longstanding attention. In recent years, deep learning techniques have demonstrated robust feature representation capabilities and led to a big leap in the development of RSOD techniques. In this era of rapid technical evolution, this review aims to present a comprehensive review of the recent achievements in deep learning based RSOD methods. More than 300 papers are covered in this review. We identify five main challenges in RSOD, including multi-scale object detection, rotated object detection, weak object detection, tiny object detection, and object detection with limited supervision, and systematically review the corresponding methods developed in a hierarchical division manner. We also review the widely used benchmark datasets and evaluation metrics within the field of RSOD, as well as the application scenarios for RSOD. Future research directions are provided for further promoting the research in RSOD.