Powered by advances in multiple remote sensing sensors, the production of high spatial resolution images provides great potential to achieve cost-efficient and high-accuracy agricultural inventory and analysis in an automated way. Lots of studies that aim at providing an inventory of the level of each agricultural parcel have generated many methods for Agricultural Parcel and Boundary Delineation (APBD). This review covers APBD methods for detecting and delineating agricultural parcels and systematically reviews the past and present of APBD-related research applied to remote sensing images. With the goal to provide a clear knowledge map of existing APBD efforts, we conduct a comprehensive review of recent APBD papers to build a meta-data analysis, including the algorithm, the study site, the crop type, the sensor type, the evaluation method, etc. We categorize the methods into three classes: (1) traditional image processing methods (including pixel-based, edge-based and region-based); (2) traditional machine learning methods (such as random forest, decision tree); and (3) deep learning-based methods. With deep learning-oriented approaches contributing to a majority, we further discuss deep learning-based methods like semantic segmentation-based, object detection-based and Transformer-based methods. In addition, we discuss five APBD-related issues to further comprehend the APBD domain using remote sensing data, such as multi-sensor data in APBD task, comparisons between single-task learning and multi-task learning in the APBD domain, comparisons among different algorithms and different APBD tasks, etc. Finally, this review proposes some APBD-related applications and a few exciting prospects and potential hot topics in future APBD research. We hope this review help researchers who involved in APBD domain to keep track of its development and tendency.