The simulation of an increasing number of important applications in porous media such as gas storage, geothermal energy production, or investigation of storage sides for nuclear waste, requires complex physical models and high spatial resolutions, but also the investigation of large-scale effects. Due to the limitations of computational resources, huge model domains often have to be simulated on relatively coarse grids. However, depending on the application, a high spatial resolution may be necessary to capture important effects, for example due to small scale heterogeneities. One solution strategy is multi-scale modeling. The idea is to decrease the number of global degrees of freedom while preserving important fine-scale features. In this work, a novel approach for multi-scale modeling of two-phase flow in porous media is developed. The method can be applied in a wide range of physical regimes, in particular, in regimes in which capillary effects have a major impact on the flow processes. In this case, many existing upscaling or multi-scale techniques, originally developed and successfully used for advection-dominated systems, fail or are not able to yield sufficiently accurate results. In the new approach, an h-adaptive grid method is combined with various local upscaling techniques. In particular, the numerical method has to be able to treat complex effective parameters like anisotropic phase permeabilities. A crucial point is the development of suitable grid-adaptation strategies to account correctly for important effects. The method is tested and proven to work for various two- and three-dimensional examples including varying heterogeneous parameter fields and different flow regimes. For discretizing the two-phase flow equations, a finite volume scheme based on the multi-point flux approximation L-method is developed and validated on various test problems. The tests show that the method is able to approximate important two-phase flow features, to account for the effects of anisotropic coefficients, and to treat hanging nodes which appear in non-conforming adaptive grids. Moreover, different numerical upscaling techniques are combined and extended to get a set of methods which enables the calculation of the effective parameters that appear in the coarse-scale equations. Using the adaptive grid finally provides a scale transfer mechanism and therefore enables a multi-scale solution. The key factor of this novel multi-scale approach is an appropriate adaptation strategy, which aims to refine and coarsen the grid such that the method is efficient and sufficiently accurate. Therefore, different adaptation indicators are suggested. Besides the so-called standard indicators, which try to minimize numerical errors in the solutions, the development of special multi-scale indicators has to be emphasized. The idea of such indicators is to take into account the validity of the upscaled parameters for the error estimation. Finally, the multi-scale concept is tested and validated on various two- and three-dimensional scenarios relating to realistic applications. The tests show that the multi-scale method performs very well for a variety of challenging heterogeneous parameter fields and for various flow regimes, ranging from the purely viscous dominated case to the capillary dominated case. Furthermore, the results show that the characteristic of saturation transport can dramatically change depending on the capillary pressure influence. Thus, it is extremely important to have efficient multi-scale models which allow us to model large-scale problems and still account for this effect correctly.