Polyurethane (PU) is widely used in construction, transportation, automotive products, decorative materials, and related industries because its molecular structure can be tailored to diverse service requirements. This versatility has stimulated growing interest in polyurethane-modified asphalt for pavement engineering. This review examines the chemical structure, reaction mechanisms, and principal synthesis routes of polyurethane-modified asphalt and discusses polyurethane-modified emulsified asphalt, polyurethane composite-modified asphalt, and polyurethane-modified asphalt mixtures. Engineering applications in permeable pavements, bridge and tunnel surfacing, as well as crack and pothole repair are also considered. The review further addresses green in situ polymerization, high-content polyurethane systems, waterborne polyurethane, interfacial adhesion, bio-based formulations, recycled asphalt mixtures, and life-cycle performance. The available evidence indicates that polyurethane can improve high-temperature stability, durability, fatigue resistance, mechanical strength, adhesion, and aging resistance. In suitable formulations, it can also reduce production temperatures and construction-related emissions. Economic feasibility, unresolved technical issues, and future research priorities are discussed at the end of the review.