Abstract Naturally fractured reservoirs (NFR), such as the large carbonate reservoirs in the Middle East, contain a major part of the world’s remaining conventional oil reserves, but recovering these is especially challenging as the fractures only constitute fluid conduits while the oil is trapped in a low-permeability rock matrix. Recovery factors are therefore difficult to estimate, permeability anisotropy is high, size and shape of drainage areas are difficult to constrain, early water breakthrough is likely to be associated with a high and irreversible water cut, and secondary recovery behaviour is unusual. Outcrop-analogue model-based discrete fracture and matrix (DFM) simulations have emerged recently, helping us to disentangle and rationalize this erratic production behaviour. They allow us to understand the emergent flow behaviour and resulting saturation patterns in NFRs. Thus, classical simulation approaches, such as dual-continua conceptualizations, can be critically evaluated and improved where they fail to capture the flow behaviour of interest. This paper discusses recent advances in DFM simulation of single- and multi-phase flow processes in geologically realistic outcrop-analogue models, and solved with finite-element (FE) and finite-volume (FV) methods. It also reviews key results from recent DFM simulation studies, in particular how new measures such as the fracture–matrix flux ratio and velocity spectra can provide new means to analyse flow behaviour in heterogeneous domains or how results from outcrop-based simulations can be used to test the suitability of conventional upscaling approaches for NFR and guide the development of new ones. We close by enlisting outstanding challenges in outcrop-based flow simulations such as the need to capture the fracture–matrix transfer processes due to capillary, gravity and viscous forces accurately, which often implies detailed grid refinement at the fracture–matrix interface and small time-steps to resolve the physical processes adequately. Thus, we explore how outcrop-based flow simulation could be applied more routinely in NFR reservoir characterization and simulation workflows.