Responsive materials, as well as active structural systems, are today widely used to develop unprecedented smart devices, sensors, or actuators; their functionalities come from the ability to respond to environmental stimuli with a detectable reaction. Depending on the responsive material under study, the triggering stimuli can have a different nature, ranging from physical (temperature, light, electric or magnetic field, mechanical stress, etc.), chemical (pH, ligands, etc.), or biological (enzymes, etc.) type. Such a responsiveness can be obtained by properly designing the meso-or macroscopic arrangement of the constitutive elements, as occurs in metamaterials, or can be obtained by using responsive materials per se, whose responsiveness comes from the chemistry underlying their microstructure. In fact, when the responsiveness at the molecular level is properly organized, the nanoscale response can be collectively detected at the macroscale, leading to a responsive material. In the present article, we review the enormous world of responsive polymers, by outlining the main features, characteristics, and responsive mechanisms of smart polymers and by providing a mechanical modeling perspective, both at the molecular as well as at the continuum scale level. We aim at providing a comprehensive overview of the main features and modeling aspects of the most diffused smart polymers. The quantitative mechanical description of active materials plays a key role in their development and use, enabling the design of advanced devices as well as to engineer the materials' microstructure according to the desired functionality.