The goals of the present review paper are; (i) to introduce experimental facilities and numerical tools applied to investigating inhomogeneously premixed flames, (ii) to summarize recent progress in revealing and understanding local phenomena (e.g. back-supported combustion or generation of flame surface area) that stem from the influence of mixture inhomogeneities on flame propagation through flammable reactants, (iii) to show state-of-the-art of unsteady multidimensional RANS and LES research into inhomogeneously premixed turbulent flames and to discuss models invoked for this purpose, and (iv) to highlight issues that still challenge researchers who develop such models. (C) 2017 Elsevier Ltd. All rights reserved.