The human world is full of things that move: people travelling, in buses and trains and cars and taxis, goods being shipped and delivered, etc. etc. Sensors for recording these movements are becoming cheaper and more widespread, from GPS-equipped mobile phones to smart commuter cards, and so there is an explosion in the amount of movement data that is available. How can this wealth of data be understood, and how can it be put to work to improve the way the world moves? I will present a system we have built, called the Space-Time Engine, for working with big data about urban mobility. It has three parts: (1) algorithms for stitching together partial or noisy observations to reconstruct a fine-grained "digital replica", (2) interactive visualizations and a query language for answering questions and building models about movement data, (3) integration with simulation and other operations-research tools to answer "what might happen?" rather than just "what did happen?" The Space-Time Engine aims to be a data science tool for users who are comfortable with Excel but not with probability or optimization theory. Based on our experience designing it, I will discuss ways in which big data might make network modeling accessible to a broader audience.