As the number of new drug candidates that are poorly soluble in water grows, new technologies that enable the enhancement of their solubility are needed. This is the case with amorphous solid dispersions (ASDs) that, nowadays, not only ensure the solubility, but can also be used to control the release rate of poorly soluble drugs. However, this dosage form must overcome the major disadvantage of ASDs, which is limited stability upon storage. Thus, a thorough knowledge on polymeric carriers that can enhance drug solubility while ensuring stability in the amorphous form is necessary. In this review, the state of the art in the application of Kollidon® VA 64 (copovidone) and Soluplus® (graft copolymer of polyvinyl caprolactam-polyvinyl acetate and poly(ethylene glycol) (PEG)) in the manufacturing of ASDs over the last 20 years is presented. Apart from the classical methods, namely solvent evaporation or melting, more advanced technologies such as pulse combustion drying, high-speed electrospinning and single-step 3D printing are described. It has been shown that both the dissolution rate (in vitro) and enhancement in bioavailability (in vivo) regarding poorly soluble active ingredients of natural or synthetic origin are possible using these matrix-forming polymers.