Despite the widespread use of plasticizers in the polymer industry, the mechanism of plasticization remains poorly understood. Industrial selection of plasticizers largely relies on semi-empirical rules and even for successful candidates, it is often difficult to answer why they outperform other molecules in terms of effectively reducing the glass transition temperature and elastic modulus of the material. In addition to plasticization efficiency, plasticizer migration is an issue that is causing increasing concern. Plasticizers that are not chemically bonded to the host polymer often migrate out of the matrix, either evaporating into the atmosphere or being absorbed into any liquids or other polymers in contact with the plastic. The loss of plasticizers over time not only causes the deterioration of material properties, it is also an environmental and safety concern. In particular, it is recently found that phthalates, the most consumed family of plasticizers on the market, are hazardous to human health. We use molecular simulation at both the full-atom and coarse-grained levels to understand the plasticization mechanism. From this knowledge, a number of molecular descriptors will be identified for a semi-quantitative prediction of the efficiency of any plasticizer based on its chemical structure. In addition, predictions will also be made on the thermodynamic compatibility between the plasticizer and its host polymer, as well as the diffusion coefficient of the plasticizer in the latter; these will help us estimate the tendency and speed of plasticizer migration. The end goal is to develop a computational protocol for screening plasticizers and finding high-performance and stable alternatives to phthalates.