In his seminal publications during 1874–1875, Jacobus Henricus van’t Hoff made the leap from tetravalent carbonTetravalent carbon (Kekulé’s theory) to tetrahedral carbonTetrahedral carbon. He recognized the stereochemical consequences of the different modes for joining tetrahedra, using this model to explain the existence of chemical structures which are non-superimposable mirrorMirror(s) images. The existence of alkeneAlkene(s) stereoisomersStereoisomers, well known at that time, was easily explained by fusing tetrahedra along one edge. Inspired by structures suggested earlier by Kekulé, van’t Hoff further extended his model to cumulated carbon structures, which were unknown in that period. He predicted the chiralityChirality of even cumulenesCumulenes such as allenesAllene(s) (derivatives of 1,2-propadiene) and the existence of cis–trans isomers for odd cumulenes such as 1,2,3-butatrienesButatriene. This chapter describes the historical evolution and realization of these models, with a focus on allenes and cumulenes. The later development of Adolph von Baeyer’s strain theoryStrain theory for cyclic carbon compounds led chemists to explore the synthesis of strained and highly reactive cyclic allenesAllene(s) and cyclic cumulenesCumulenes as an extension of van’t Hoff’s theories. Some historical milestones in this field are described.