 This is Hurricane Irma, one of the strongest hurricanes of 2017. It caused tremendous damage in the Caribbean and in Florida. How will hurricanes change in a changing climate? And what about other extreme events, such as floodings or droughts? To answer these questions we need long-standing records, such as a record of the Galveston Hurricane of 1900, the Lucerne flooding of 1910, or the flooding of river Thames in 1928. Today we have many observations from weather stations, ships, buoys and satellites that measure the weather systems in different spectral bands from different angles and at different times. In the past, however, observations were very sparse and we only have few records. Moreover, these records are spread all over the world in archives. To make these valuable records accessible, many research projects are working on digitalising them. So how can we reconstruct the weather for such past events with the few records we have? Let's show this using a football kick. Assume the trajectory of the ball is the development of the weather over time. In the present day, we are continuously observing the weather all over the world, much like filming the football kick, to get uninterrupted data of its change. Reconstruction here is no problem, since we know the ball's position at various times. In the past, however, where observations were rare, the film analogy is not accurate. It's more like we only have three different pictures of the football kick as our past records. This makes reconstruction rather tricky. To solve this problem, we need a model. Models are based on physical equations, which are transformed into algorithms and finally into computer code. This code is then run on supercomputers, and the results are forecasts or reconstructions. Those are not perfect, but they do obey the laws of physics. For the case of the football kick, the model is the inclined throw. This model, however, is a bit too simple. If we also account for friction, it already looks more realistic. Of course, we could still improve it in many ways, but for the sake of demonstration, it will do. The model on its own does not tell us the ball's trajectory or any concrete locations the ball occupied. All it gives us is a framework for how the ball could behave. That is why we need the starting conditions and the photographs. Combining them with the model enables us to initiate the reconstruction. There are three different strategies to accomplish this. The particle filter method, the Kalman filter, and 4DVAR. The approach of the particle filter is to make many simulations and use the photos to pick the best-fitting one. We start with many simulations and stop them once they reach the first photograph. There, only the one closest to the photograph is kept. Because there is an error both in the model and in the photograph, we perturb that state a little and then start new simulations again. We repeat this step at the second and again at the third photograph. In the end, the four best segments make up the reconstruction of the ball's trajectory. The second approach, steering the model simulation, is called the Kalman filter. One of its first uses was landing on the moon. In the case of the football kick, we start with a reasonable forecast, stop it at the first photograph, compare it with the photograph, and adjust the model state accordingly. The adjustment accounts for the error of the photograph and the error of the model. It can be understood as some sort of weighted average. From this corrected state, we start the next forecast and repeat the steps for all photographs, so we're continually steering our model simulation using the photographs. In the end, we again have four segments that make up the ball's trajectory. Unlike the other two methods, the third approach, 4DVAR, does not segment the trajectory. It tries to find the ideal starting conditions for one uninterrupted trajectory. We again begin with reasonable starting conditions, make a forecast and note the deviation of the first photograph. We do not, however, stop or adjust the simulation, but go on to the second and third photograph, each time noting the deviation between photograph and simulation. Each of these deviations gives us an equation. We solve these equations backwards using a linearized version of the model, which gives us the ideal starting positions. We now make a new forecast based on these starting positions, which then gives us our reconstruction. All three methods require comparing a three-dimensional model with a two-dimensional photograph. The only way this can be done is to simulate the photograph inside the model. In this way, the correction determined on the two-dimensional photograph then automatically corrects the entire three-dimensional model state. The same methods are applied to make weather reconstructions. We obviously don't use the inclined throw, but a complex weather forecast model. The same way we used photographs in the football example, we now take surface pressure measurements. These measurements date back to the 18th century and provide us with a series of observations that we can combine with the model. Using the ensemble Kalman filter and 4D var, we now initiate our reconstruction. The end product is a so-called re-analysis. Despite sparse observation, we now have three-dimensional, continuous data for the weather of the past and a better understanding of today's extreme events.