  The last decade has seen a strong increase of research into flows in
fractured porous media, mainly related to subsurface processes, but also in
materials science and biological applications. Connected fractures totally
dominate flow-patterns, and their representation is therefore a critical part
in model design. Due to the fracture's characteristics as approximately planar
discontinuities with an extreme size to width ratio, they challenge standard
macroscale mathematical and numerical modeling of flow based on averaging.
Thus, over the last decades, various, and also fundamentally different,
approaches have been developed. This paper reviews common conceptual models and
discretization approaches for flow in fractured porous media, with an emphasis
on the dominating effects the fractures have on flow processes. In this
context, the paper discuss the tight connection between physical and
mathematical modeling and simulation approaches. Extensions and research
challenges related to transport, multi-phase flow and fluid-solid interaction
are also commented on.
