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The rapid development of deep learning has made a great progress in image segmentation, one of the fundamental tasks of computer vision. However, the current segmentation algorithms mostly rely on the availability of pixel-level annotations, which are often expensive, tedious, and laborious. To alleviate this burden, the past years have witnessed an increasing attention in building label-efficient, deep-learning-based image segmentation algorithms. This paper offers a comprehensive review on label-efficient image segmentation methods. To this end, we first develop a taxonomy to organize these methods according to the supervision provided by different types of weak labels (including no supervision, inexact supervision, incomplete supervision and inaccurate supervision) and supplemented by the types of segmentation problems (including semantic segmentation, instance segmentation and panoptic segmentation). Next, we summarize the existing label-efficient image segmentation methods from a unified perspective that discusses an important question: how to bridge the gap between weak supervision and dense prediction -- the current methods are mostly based on heuristic priors, such as cross-pixel similarity, cross-label constraint, cross-view consistency, and cross-image relation. Finally, we share our opinions about the future research directions for label-efficient deep image segmentation.