A coupled description of flow and thermal-reactive transport is spanning a wide range of scales in space and time, which often introduces a significant complexity for the modelling of such processes. Subsurface reservoir heterogeneity with complex multi-scale features increases the modelling complexity even further. Traditional Algebraic Multiscale techniques are usually focused on the accuracy of the pressure solution and often ignore the transport. Improving the transport solution can however be quite significant for the performance of the simulation, especially in complex applications related to thermal-compositional flow. The use of an Adaptive Mesh Refinement enables the grid to adapt dynamically during the simulation, which facilitates the efficient use of computational resources. This is especially important in applications with reactive flow and transport where the region requires high-resolution calculations as often localized in space. In this work, the aim is to develop an Adaptive Mesh Refinement framework for general-purpose reservoir simulation. The approach uses a multi-level connection list and can be applied to fully unstructured grids. The adaptivity of the grid in the developed framework is based on a hierarchical approach. First, the fine-scale model is constructed, which accurately approximates all reservoir heterogeneity. Next, a global flow-based upscaling is applied, where an unstructured partitioning of the original grid is created. Once the full hierarchy of levels is constructed, the simulation is started at the coarsest grid. Grid space refinement criteria can be developed specifically for a particular application of interest. The multi-level connectivity lists are redefined at each timestep and used as an input for the next. The developed Adaptive Mesh Refinement framework was implemented in Delft Advanced Research Terra Simulator which uses the Operator-Based Linearization technique. The performance of the proposed approach is illustrated for several applications, including hydrocarbon production, geothermal energy extraction and subsurface storage.