A self-driving vehicle (SDV) must be able to perceive its surroundings and predict the future behavior of other traffic participants. Existing works either perform object detection followed by trajectory forecasting of the detected objects, or predict dense occupancy and flow grids for the whole scene. The former poses a safety concern as the number of detections needs to be kept low for efficiency reasons, sacrificing object recall. The latter is computationally expensive due to the high-dimensionality of the output grid, and suffers from the limited receptive field inherent to fully convolutional networks. Furthermore, both approaches employ many computational resources predicting areas or objects that might never be queried by the motion planner. This motivates our unified approach to perception and future prediction that implicitly represents occupancy and flow over time with a single neural network. Our method avoids unnecessary computation, as it can be directly queried by the motion planner at continuous spatio-temporal locations. Moreover, we design an architecture that overcomes the limited receptive field of previous explicit occupancy prediction methods by adding an efficient yet effective global attention mechanism. Through extensive experiments in both urban and highway settings, we demonstrate that our implicit model outperforms the current state-of-the-art. For more information, visit the project website: https://waabi.ai/research/implicito.