In this talk we discuss how standard results about non-commutative resolutions of finite groups generalize to arbitrary reductive groups. We show in particular that quotient singularities for reductive groups always have non-commutative resolutions in an appropriate sense. Moreover we exhibit a large class of such singularities which have (twisted) non-commutative crepant resolutions (NCCRs). We show that (twisted) NC(C)Rs exist for determinantal varieties of symmetric and skew-symmetric matrices. Joint work with Michel Van den Bergh.