Grasping is natural for humans. However, it involves complex hand configurations and soft tissue deformation that can result in complicated regions of contact between the hand and the object. Understanding and modeling this contact can potentially improve hand models, AR/VR experiences, and robotic grasping. Yet, we currently lack datasets of hand-object contact paired with other data modalities, which is crucial for developing and evaluating contact modeling techniques. We introduce ContactPose, the first dataset of hand-object contact paired with hand pose, object pose, and RGB-D images. ContactPose has 2306 unique grasps of 25 household objects grasped with 2 functional intents by 50 participants, and more than 2.9 M RGB-D grasp images. Analysis of ContactPose data reveals interesting relationships between hand pose and contact. We use this data to rigorously evaluate various data representations, heuristics from the literature, and learning methods for contact modeling. Data, code, and trained models are available at https://contactpose.cc.gatech.edu.