Vegetable oils (VOs) are one of the most promising renewable sources of phase change materials (PCMs). Although several studies have been published, there are no comprehensive reviews of VO-based PCMs or the structure-property relationships governing their thermal behavior. This critical review systematically organizes the published literature on VO-based PCMs focusing on the role that structural elements play in the establishment of thermal properties relevant to thermal energy storage (TES). Thermal properties such as thermal stability, phase change temperature, enthalpy, entropy and thermal conductivity are the functional parameters examined within the context of structure. The empirical correlations between structure and thermal functionality of PCMs are assembled in predictive relationships, drawing a unified picture of the rules that govern their phase behavior. Relationships such as the effect of fatty chain length, number and types of functional groups, symmetry, and isomerism on the molecule's thermal properties were explored. Phase change temperatures and enthalpies of linear saturated PCMs with monofunctional group follow exponential rise to maximum functions while the entropy increases linearly with increasing carbon chain length. The ranges for phase change temperature, enthalpy, entropy, thermal stability, and thermal conductivity for all the VO-based PCMs in this work were --100-300 ?C, 90-270 J/g, 100-500 J/mol/K, 95-350 ?C and 0.1-0.4 W/mK respectively. The gathered knowledge is critically discussed to provide directions for future PCM research and development.