Summary of the thesis This thesis addresses simulation of flow and transport of fluids and fluid components in heterogeneous and fractured porous media. Reservoir simulation is a key component in several engineering applications, such as oil recovery, groundwater hydrology, nuclear waste disposal, and geological CO2 storage. In this thesis we are primarily concerned with hetereogenous and fractured reservoirs, which pose great challenges to the mathematical methods used to solve the governing equations. We consider two different approaches to model flow in such reservoirs. The first approach is by upscaling, which is a technique to calculate effective (averaged) property values of a heterogeneous bulk. Upscaling is used to incorporate important small scale heterogeneities into a model on a largerscale. This may effectively reduce the model complexity, and in turn lead to lower computation time and less memory requirements, while at the same time retain the global flow pattern. In particular, we consider steady-state upscaling, which is a local flow-based method to upscale two-phase properties. We study the rate dependency of the upscaled properties and validate steady-state upscaling by comparing simulation results on fine-scaled and upscaled models of a representative fluvial reservoir. The second approach is to model flow in fractured porous media by representing the fractures explicitly as lower-dimensional surfaces embedded in the surrounding material. This is computationally more expensive than upscaling techniques, but gives a more detailed flow simulation. We present a novel mathematical model that is simple to implement and handles complex fracture geometry. The flow problem is solved by a continuous Galerkin finite element method followed by a developed postprocessing step to ensure local conservation of mass, while the transport problem is solved by a low order finite volume method.