Abstract This paper reviews recent advances in understanding the structure of turbulent partially premixed and stratified flames. The term “partially premixed” refers here to compositionally inhomogeneous mixtures that include flammable and non-flammable fluid while “stratified” combustion refers to a reacting front propagating through a range of compositions within the flammable limits. An overview of relevant laminar flame concepts is first introduced. In laminar partially premixed flames, the interaction between rich and lean mixtures is significant leading to improvement in the flame’s resistance to extinction by straining. In lean back-supported laminar stratified flames, the flux of excess heat and radicals into the lean fluid results in higher flame speeds, broader reaction zones, and extended flammability limits compared to homogeneous counterparts. Rich stratified flames are more complex due to the combined fluxes of heat as well as reactive species such as H2 and CO. Recent research in turbulent partially premixed as well as stratified flames is reviewed. Detailed measurements in burners representative of those found in gas turbine combustors show that partial premixing at the lifted flame base increases with instability. Well-characterised laboratory burners where different fuel concentration gradients may be imposed at the jet exit plane show improved flame stability due to mixed-mode combustion. Maximum stability is reached at some optimum level of compositional inhomogeneity. Highly resolved measurements in turbulent stratified flames show that the mass fractions of CO and H2 increase with stratification; a result that is consistent with laminar flame studies. Such experiments are, however, very difficult and require multi-level conditioning of the data. The paper concludes with a brief review of potential numerical approaches employed in the calculations of turbulent flames with inhomogeneous inlet conditions. A key challenge here is to reproduce the effects of increasing levels of stratification and/or inhomogeneity on the compositional structure of turbulent flames.