▪ Abstract  Efficiently and accurately solving the equations governing fluid flow in oil reservoirs is very challenging because of the complex geological environment and the intricate properties of crude oil and gas at high pressure. We present these challenges and review successful and promising solution approaches. We discuss in detail the modeling of fluid flow in reservoirs with strongly varying rock properties. This requires subgrid-scale models that accurately represent the flow physics due to fine-scale fluctuations. A second focus is on the complex multiphase, multicomponent systems that describe miscible gas injection processes for enhanced oil recovery and CO₂ sequestration.