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In recent years, supervised learning has been widely used in various tasks of optical remote sensing image understanding, including remote sensing image classification, pixel-wise segmentation, change detection, and object detection. The methods based on supervised learning need a large amount of high-quality training data and their performance highly depends on the quality of the labels. However, in practical remote sensing applications, it is often expensive and time-consuming to obtain large-scale data sets with high-quality labels, which leads to a lack of sufficient supervised information. In some cases, only coarse-grained labels can be obtained, resulting in the lack of exact supervision. In addition, the supervised information obtained manually may be wrong, resulting in a lack of accurate supervision. Therefore, remote sensing image understanding often faces the problems of incomplete, inexact, and inaccurate supervised information, which will affect the breadth and depth of remote sensing applications. In order to solve the above-mentioned problems, researchers have explored various tasks in remote sensing image understanding under weak supervision. This paper summarizes the research progress of weakly supervised learning in the field of remote sensing, including three typical weakly supervised paradigms: 1) Incomplete supervision, where only a subset of training data is labeled; 2) Inexact supervision, where only coarse-grained labels of training data are given; 3) Inaccurate supervision, where the labels given are not always true on the ground.