The extracellular space has an ambiguous role in neuroscience. It is present in every physiologically relevant system and often used as a measurement site in experimental recordings, but it has received subordinate attention compared to the intracellular domain. In computational modeling, it is often regarded as a passive, homogeneous resistive medium with a constant conductivity, which greatly simplifies the computation of extracellular potentials. However, recent studies have shown that local ionic diffusion and capacitive effects of electrically active membranes can have a substantial impact on the extracellular potential. These effects can not be described by traditional models, and they have been subject to theoretical and experimental analyses. We strive to give an overview over recent progress in modeling the extracellular space with special regard towards the concentration and potential dynamics on different temporal and spatial scales. Three models with distinct assumptions and levels of detail are compared both theoretically and by means of numerical simulations: the classical volume conductor (VC) model, which is most frequently used in form of the line source approximation (LSA); the very detailed, but computationally intensive Poisson-Nernst-Planck model of electrodiffusion (PNP); and an intermediate one called the electroneutral model (EN). The results clearly show that there is no one model for all applications, as they show significantly different responses especially close to neuronal membranes. Finally, we list some common use cases for model simulations and give recommendations on which model to use in each situation.