With ITER, the largest tokamak ever built, and the growing number of fusion energy startups in the world, the need for numerical simulations has never been more crucial to progress towards the successful operation of fusion reactors. From fundamental plasma physics to engineering, a hierarchy of models exists from high-fidelity (gyro-)kinetic models in (5D) 6D to 0D fluid transport models. In this paper, we review the state-of-the-art of 3D turbulence fluid simulations in edge tokamak configurations. The widely used drift-reduced Braginskii equations are introduced together with the dedicated boundary conditions modelling plasma wall interactions. If until recently most of the models were focused on electrostatic turbulence driven by interchange-like instabilities, in recent years models have incorporated electromagnetic effects allowing fluctuations of the magnetic field. Specific features of the edge plasma configurations, which make these equations specially challenging to resolve and stressful for the numerical methods, are detailed. In particular, the strong anisotropy of the flow as well as the complex geometric characteristics lead to the development of dedicated discretization schemes and meshing, which are implemented in state-of-the-art codes reviewed here. It appears that the latter can be differentiated by their mesh construction as well by the manner in which they handle parallel gradients (aligned or not along the magnetic field). The review shows that no consensus on the optimal combination between meshing and discretization schemes, if it exists, has been found. Finally, examples of recent achievements show that 3D turbulence simulations of medium-sized tokamaks are currently achievable, but that ITERsize tokamaks and thermonuclear plasmas still require significant progress.