Basic plasma transport properties in island divertors are compared to those of standard tokamak divertors. A realistic plasma transport modelling of high-density discharges in island divertors has become possible by implementing a self-consistent treatment of impurity transport in the EMC3-EIRENE code. In contrast to standard tokamak divertors, the code predicts no high recycling prior to detachment, with the downstream density never exceeding the upstream density. This is mainly due to momentum losses arising from the cross-field transport associated with the specific island divertor geometry. This momentum loss is effective already at low densities, high temperatures and is responsible for the high upstream densities needed to achieve detachment. Numerical scans of carbon concentration for high-density plasma typically show first a smooth, then a sharp increase of the carbon radiation, the latter being accompanied by a sharp drop of the downstream temperature and density indicating detachment transition. The jumps of the radiation and temperature are due to a thermal instability associated with the form of the impurity cooling rate function and can be reproduced by a simple 1D radial energy model based on cross-field transport and impurity losses. This model is used as a guideline to illustrate and discuss the detachment physics in details, including detachment condition and thermal instability. Major EMC3-EIRENE code predictions have been verified by the first W7-AS divertor experiments. A comparison of calculations and measurements is presented for high-density, high-power W7-AS divertor discharges and the physics related to rollover and detachment is discussed in detail. The code has been recently extended to general SOL configurations with open islands and arbitrary ergodicity by using a new highly accurate field-line mapping technique. The method correctly reproduces flux surfaces and islands over a high number of toroidal field periods, thus ensuring a clear distinction between parallel and radial transport. The technique has been tested successfully on W7-AS, W7-X, LHDand TEXTOR DED, and first applied to solve the coupled heat conduction equations for a typical ergodic W7-AS configuration.