With Large Helical Device (LHD) and Wendelstein 7-X (W7-X), the development of helical devices is now taking a large step forward on the path to a steady-state fusion reactor. Important issues that need to be settled in these machines are particle flux and heat control and the impact of divertors on plasma performance in future continuously burning fusion plasmas. The divertor concepts that will initially be explored in these large machines were prepared in smaller-scale devices like Heliotron E, Compact Helical System (CHS), and Wendelstein 7-AS (W7-AS). While advanced divertor scenarios relevant for W7-X were already studied in W7-AS, other smaller-scale experiments like Heliotron-J, CHS, and National Compact Stellarator Experiment will be used for the further development of divertor concepts. The two divertor configurations that are being investigated are the helical and the island divertor, as well as the local island divertor, which was successfully demonstrated on CHS and just went into operation on LHD. At present, on its route to a fully closed helical divertor, LHD operates in an open helical divertor configuration. W7-X will be equipped right from the start with an actively cooled discrete island divertor that will allow quasi-continuous operation. The divertor design is very similar to the one explored on W7-AS. For sufficiently large island sizes and not too long field line connection lengths, this divertor gives access to a partially detached quasi-steady-state operating scenario in a newly found high-density H-mode operating regime, which benefits from high energy and low impurity confinement times, with edge radiation levels of up to 90% and sufficient neutral compression in the subdivertor region (>10) for active pumping. The basic physics of the different divertor concepts and associated implementation problems, like asymmetries due to drifts, accessibility of essential operating scenarios, toroidal asymmetries due to symmetry breaking error fields, etc., are discussed.