If we make the term "higher-dimensional varieties" mean something like dimension greater or equal than, say, 10, then there aren't too many families of varieties that are suitable for studying its rational points. A natural family of varieties that transcends in a certain sense this dimension problem is that of homogeneous spaces, that is, varieties admitting a transitive action of an algebraic group. For these varieties, the algebraic structure and the behavior of the rational points of the group itself can give us lots of information about the rational points of the homogeneous space, in particular (but not uniquely) via the use of the (usually non-abelian) Galois cohomology of these algebraic groups. Thus, if one is concerned for example with the problem of the Hasse principle (HP) or with weak approximation (WA), one can usually translate this statements into Galois cohomology statements, many of which have been proved in the last 50 years. In this trend, the deepest result up to date is probably that of Borovoi, who proved in 1996 that the Brauer-Manin obstruction to HP and WA is the only obstruction for homogeneous spaces under linear algebraic groups (over a number field) with connected or abelian stabiliser (the second case needing an aditional technical condition). This clearly leaves the open question: what about disconnected stabilisers ? In particular, for "simplicity", what about finite (non-abelian) stabilisers ? These questions seem to be of a completely different nature of those already solved (compare for instance, over an algebraically closed field, the classification of connected reductive groups with that of finite groups !). However, if one believes in Colliot-Thélène's conjecture on the Brauer-Manin obstruction to HP and WA being the only obstruction for unirational varieties, of which homogeneous spaces are a particular example, this questions should have the same answer. This is the problem I'm interested in today but, whether one cares about HP and WA or, for instance, integral points, strong approximation, problems in positive characteristic or any other arithmetico-geometric topic, homogeneous spaces have all the right to be studied in this workshop.