This article examines the conceptual framework of the crystal network of fat materials in the context of its many hierarchical levels, from the molecular/nanostructural (10
−9
m) level all the way to the submillimeter (10
−6
m) length scale. Included in this article is a discussion on thermal properties of triacylglycerols, phase behavior, crystallization thermodynamics, crystallization into single crystals (crystalline nanoplatelets), aggregation of single crystals, rheology, and derivations of material properties based on the microstructure. Introductory concepts are provided, and for more detailed scholarship, readers are referred to an ample list of specialist texts and papers on the subject.