This is a synoptic overview of a selection of works dealing with single diffusive structures, with their mutual interaction in simple flows and their statistical modeling in complex flows. The focus is on reacting conditions pertaining to gaseous diffusion flames, but isothermal structures are also described when they are of some conceptual interest. This paper considers only few representative works for each subject, which are functional in explaining the key characteristics of the diffusive structures. The extension, given to single subjects, is not weighed according to the number of related publications but on the relevance to the basic understanding of the general framework concerning diffusion flames. One-dimensional structures are first discussed. They are ordered according to the number of balance equation terms needed for their description. Two-dimensional (2D) structures are then introduced following an order based on their convolution level. Some pioneering work on three-dimensional structures is further quoted. The temporal evolution of simple structures in quiescent or simple flowing 2D systems is considered. The latter case is exploited to present classification of diffusion-controlled mixing regimes. Modeling characterization approach of turbulent diffusion flames is also described in order to yield a self-sufficient didactic presentation. The approach based on the flame surface density model is specifically discussed because of its potential use in the determination of qualitative and quantitative features of simple diffusion flames.