Scientists have sought for over two decades to incorporate the necessary attributes of transparency, stability, and high nonlinear susceptibilities into optimized organic or organometallic chromophores for third-order nonlinear optical (NLO) applications. These investigations have provided an ever-expanding understanding of structure-function relationships for the second hyperpolarizability gamma and the bulk third-order nonlinear optical susceptibility chi((3)) in organic materials, which are reviewed herein. Contributing to this understanding are the studies of the third-order NLO properties displayed by an array of structurally related organic chromophores based on the conjugated carbon skeletons of hex-3-ene-1,5-diynes (1,2-diethynylethenes, DEEs) and 3,4-diethynylhex-3-ene-1,5-diynes (tetraethynylethenes, TEEs). A comprehensive series of donor (D) and/or acceptor (A) substituted derivatives of DEEs and TEEs has been measured by third-harmonic generation (THG) experiments, and the investigations on these one-and two-dimensionally conjugated chromophores have provided fundamental insight into routes leading to enhanced optical nonlinearities. The molecular characteristics identified to impact the second hyperpolarizability gamma include conjugation length, heteroaromatic conjugation, degree of D/A substitution, cis, trans, and geminal D/A conjugation, and molecular asymmetry. A comparison of NLO properties for small molecular systems to those of a number of larger oligomers based on the DEE and TEE framework is also presented.