Polymer modification of asphalt binders and the integration of recycled plastics in asphalt mixtures have become central strategies in enhancing pavement durability, reducing maintenance costs, and supporting sustainability goals. This review consolidates recent advances (2020–2025) in polymer-modified asphalt (PMA) systems, encompassing elastomeric and plastomeric modifiers, recycled plastic incorporation, performance indicators, rheological characteristics, and environmental implications. The work also identifies emerging trends in multi-factor aging studies, morphology analysis, and rheological characterization (e.g., MSCR, DSR, and BBR testing). Case studies and life-cycle assessments (LCA) demonstrate significant mechanical and ecological benefits of polymer and plastic modifiers, while compatibility and microplastic release remain active challenges.