Learning to re-identify or retrieve a group of people across non-overlapped camera systems has important applications in video surveillance. However, most existing methods focus on (single) person re-identification (re-id), ignoring the fact that people often walk in groups in real scenarios. In this work, we take a step further and consider employing context information for identifying groups of people, i.e., group re-id. On the one hand, group re-id is more challenging than single person re-id, since it requires both a robust modeling of local individual person appearance (with different illumination conditions, pose/viewpoint variations, and occlusions), as well as full awareness of global group structures (with group layout and group member variations). On the other hand, we believe that person re-id can be greatly enhanced by incorporating additional visual context from neighboring group members, a task which we formulate as group-aware (single) person re-id. In this paper, we propose a novel unified framework based on graph neural networks to simultaneously address the above two group-based re-id tasks, i.e., group re-id and group-aware person re-id. Specifically, we construct a context graph with group members as its nodes to exploit dependencies among different people. A multi-level attention mechanism is developed to formulate both intra-group and inter-group context, with an additional self-attention module for robust graph-level representations by attentively aggregating node-level features. The proposed model can be directly generalized to tackle group-aware person re-id using node-level representations. Meanwhile, to facilitate the deployment of deep learning models on these tasks, we build a new group re-id dataset which contains more than 3.8K images with 1.5K annotated groups, an order of magnitude larger than existing group re-id datasets. Extensive experiments on the novel dataset as well as three existing datasets clearly demonstrate the effectiveness of the proposed framework for both group-based re-id tasks.