Reducing the complexity of the pipeline of instance segmentation is crucial for real-world applications. This work addresses this issue by introducing an anchor-box free and single-shot instance segmentation framework, termed PolarMask, which reformulates the instance segmentation problem as predicting the contours of objects in the polar coordinate, with several appealing benefits. (1) The polar representation unifies instance segmentation (masks) and object detection (bounding boxes) into a single framework, reducing the design and computational complexity. (2) Two modules are carefully designed (i.e. soft polar centerness and polar IoU loss) to sample high-quality center examples and optimize polar contour regression, making the performance of PolarMask does not depend on the bounding box prediction results and thus becomes more efficient in training. (3) PolarMask is fully convolutional and can be easily embedded into most off-the-shelf detection methods. To further improve the accuracy of the framework, a Refined Feature Pyramid is introduced to further improve the feature representation at different scales, termed PolarMask++. Extensive experiments demonstrate the effectiveness of both PolarMask and PolarMask++, which achieve competitive results on instance segmentation in the challenging COCO dataset with single-model and single-scale training and testing, as well as new state-of-the-art results on rotate text detection and cell segmentation. We hope the proposed polar representation can provide a new perspective for designing algorithms to solve single-shot instance segmentation. The codes and models are available at: github.com/xieenze/PolarMask.