The present invention relates to polymeric plasticizer compositions made from an aromatic acid source, a glycol, and a C4-C36 monocarboxylic acid, or ester or anhydride thereof. The aromatic acid source can include polymeric materials such as recycled polyethylene terephthalate (PET). The present invention also relates to methods for making the polymeric plasticizer compositions, to methods of plasticizing polymeric materials, and to plasticized polymeric compositions. The polymeric plasticizers are useful for plasticizing various polymers, such as thermoplastic polymers, including, for example, polyvinyl chloride (PVC). The polymeric plasticizers provide a sustainable alternative to conventional phthalate ester plasticizers, such as diisooctyl phthalate (DOP).