Imagine you are tracking a moving object with a noisy radar. While it is happening, you can only use the measurements you have so far — that is filtering. But later, once the whole track is recorded, you can go back and use future measurements to improve your earlier position guesses. That is smoothing. In this chapter we learn how to refine the whole history of a state‑space model, fill in data gaps, and recover the hidden random shocks that pushed the system along.