Polymer materials have been widely used in industrial, agricultural, engineering, medical, electronic, and biological fields because of their excellent and diverse properties (e.g., mechanical, optical, electrical, and adhesive properties). The adhesion of polymer materials can affect the stability, alter the surface chemistry, change the surface structure, and influence the performance of the materials. It is of both fundamental and practical importance to understand the adhesion behaviors and interaction mechanisms of polymer surfaces and thin films for the development of new functional polymers and their applications. In this article, the fundamentals of surface energy, adhesion energy, and classical contact mechanics models are presented first, and the commonly used nanomechanical techniques for quantifying the intermolecular and surface interactions of polymers, including the surface forces apparatus (SFA) and atomic force microscope (AFM), are introduced. The advances in the adhesion of surfaces and thin films of various polymers (e.g., elastomers, glassy polymers) are reviewed. The effects of various factors, including the molecular weight, temperature, separation rate, and surface roughness, on the adhesion behaviors of these polymer surfaces and thin films are discussed. Their liquid- to solid-like behaviors during approach and detachment processes are shown. Several commonly applied methodologies used to modulate polymer adhesion are also introduced. Some recent applications based on polymer adhesion, remaining challenging issues, and future perspectives are also presented.