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Detecting pedestrians and predicting future trajectories for them are critical tasks for numerous applications, such as autonomous driving. Previous methods either treat the detection and prediction as separate tasks or simply add a trajectory regression head on top of a detector. In this work, we present a novel end-to-end two-stage network: Spatio-Temporal-Interactive Network (STINet). In addition to 3D geometry modeling of pedestrians, we model the temporal information for each of the pedestrians. To do so, our method predicts both current and past locations in the first stage, so that each pedestrian can be linked across frames and the comprehensive spatio-temporal information can be captured in the second stage. Also, we model the interaction among objects with an interaction graph, to gather the information among the neighboring objects. Comprehensive experiments on the Lyft Dataset and the recently released large-scale Waymo Open Dataset for both object detection and future trajectory prediction validate the effectiveness of the proposed method. For the Waymo Open Dataset, we achieve a bird-eyes-view (BEV) detection AP of 80.73 and trajectory prediction average displacement error (ADE) of 33.67cm for pedestrians, which establish the state-of-the-art for both tasks.