A simple replacement of standard PT2 by more sophisticated correlation models from wave-function theory does not seem to lead to a notable improvement in accuracy despite the higher cost. 518 Some recent efforts to develop efficient models that go beyond PT2 for double-hybrid approximations have led to some encouraging schemes for further progress. (4.1.10) Kaupp and Arbuznikov : One generalization of the concept of hybrid functionals that tries to account for local differences in the relative importance of exchange and correlation as well as for the differing spatial demands of different property operators is to use position-dependent Hartree-Fock exchange admixture in local hybrid functionals (LHs). While this introduces the ambiguities of locally mixing exchange-energy densities (the "gauge-problem" of LHs ) and some (manageable) additional requirements regarding two-electron integrals compared with standard ("global") hybrids, the advantages of position-dependent exchange admixtures for various properties depending on different regions of space have been demonstrated. These advantages extend also to TDDFT computations of various types of excitations, including core, valence, and Rydberg excitations, with particularly good performances for triplet excitations. In general, LHs give extra flexibility to balance minimal self-interaction or delocalization errors in some regions of space with the simulation of left-right correlation in bonds. LHs can be further extended in various directions by combining with range separation (e.g., local range separation and rangeseparated LHs 535,536 ), by adding dispersion either via correction terms or via nonlocal van-der-Waals functionals, potentially by adding nonlocal rung-5 correlation contributions, or by adding corrections for strong correlation.