Amorphous solid dispersions (ASDs) have emerged as widespread formulations for drug delivery of poorly soluble active pharmaceutical ingredients (APIs). Predicting the API solubility with various carriers in the API–carrier mixture and the principal API–carrier non-bonding interactions are critical factors for rational drug development and formulation decisions. Experimental determination of these interactions, solubility, and dissolution mechanisms is time-consuming, costly, and reliant on trial and error. To that end, molecular modeling has been applied to simulate ASD properties and mechanisms. Quantum mechanical methods elucidate the strength of API–carrier non-bonding interactions, while molecular dynamics simulations model and predict ASD physical stability, solubility, and dissolution mechanisms. Statistical learning models have been recently applied to the prediction of a variety of drug formulation properties and show immense potential for continued application in the understanding and prediction of ASD solubility. Continued theoretical progress and computational applications will accelerate lead compound development before clinical trials. This article reviews in silico research for the rational formulation design of low-solubility drugs. Pertinent theoretical groundwork is presented, modeling applications and limitations are discussed, and the prospective clinical benefits of accelerated ASD formulation are envisioned.