The research presented in this thesis aims at improving computer models that allow simulations of water, oil and gas flows in subsurface petroleum reservoirs. This is done by integrating, or assimilating, measurements into physics-bases models. In recent years petroleum technology has developed rapidly. Nowadays wells can be drilled to a depth of up to 10 km, not just vertically, but also at an angle, horizontally or with branches. Moreover, downhole valves can be installed which can be opened or closed from the surface and advanced sensors can be placed in the subsurface. This technology has the potential to drain petroleum reservoirs much more efficiently. In order to do so, the technology needs to be used sensibly, which requires adequate knowledge of subsurface physical processes. Large amounts of measurements can contribute to this, but conventional methods are often ad hoc and not suited to handle the large amounts of data that are available nowadays. Good "data assimilation" methods are very important to ensure that the growing demand for energy in the near future can be met. The objective of this thesis is to apply data assimilation techniques, invented and developed in other areas of research, to petroleum reservoir engineering, to modify them to be better suited for their new application, and to investigate how they can help to integrate both production data and seismic data to support decision-making in petroleum reservoir management.