Poor aqueous solubility remains a limiting step for many recently discovered active pharmaceutical ingredients (API), especially the drugs that are classified under the Biopharmaceutics Classification System (BCS) Class II and IV. These compounds exhibit poor dissolution in gastrointestinal fluids which leads to limited oral bioavailability.  One of the strategies that has been studied to combat this challenge is Amorphous solid dispersion (ASD), which acts by improving the drug solubility through molecular dispersion in polymeric carriers. However, the efficacy of ASDs is significantly dependent on the ability of the recruited polymer to maintain the drug in an amorphous state and ensure physical and chemical stability for a long term. Therefore, there is a great interest in rational methods to guide this selection. In this review, the critical criteria involved in polymer screening, including drug-polymer interaction, miscibility along with glass transition temperature (Tg), and hygroscopicity, are discussed. Experimental and analytical techniques ranging from film casting and precipitation inhibition to Differential Scanning Calorimetry (DSC), X-ray Powder Diffraction (XRPD), Fourier Transform infrared (FTIR), and Nuclear Magnetic Resonance (NMR). Gordon–Taylor (G-T) equation, and Flory-Huggins (F-H) theory, among other methods, are also discussed as part of theoretical approaches. Furthermore, the review examines advanced computational tools such as molecular dynamics simulations (MDs) and machine learning (ML) models, which provide new opportunities for predictive formulation design, in addition to some of their strengths and limitations.