Semantic keypoints provide concise abstractions for a variety of visual understanding tasks. Existing methods define semantic keypoints separately for each category with a fixed number of semantic labels in fixed indices. As a result, this keypoint representation is in-feasible when objects have a varying number of parts, e.g. chairs with varying number of legs. We propose a category-agnostic keypoint representation, which combines a multi-peak heatmap (StarMap) for all the keypoints and their corresponding features as 3D locations in the canonical viewpoint (CanViewFeature) defined for each instance. Our intuition is that the 3D locations of the keypoints in canonical object views contain rich semantic and compositional information. Using our flexible representation, we demonstrate competitive performance in keypoint detection and localization compared to category-specific state-of-the-art methods. Moreover, we show that when augmented with an additional depth channel (DepthMap) to lift the 2D keypoints to 3D, our representation can achieve state-of-the-art results in viewpoint estimation. Finally, we show that our category-agnostic keypoint representation can be generalized to novel categories.