It is well known that the properties of polymeric materials depend strongly upon their chemical structure. Other more specific factors that may be related to the chemical structure also determine the macroscopic behaviour of such materials, namely the relative position of the different segments of the polymeric chain, the molecular architecture (molecular weight distribution, branching, copolymer organisation, cross-linking extent, etc.), the crystalline environment and the pressure/temperature conditions. All these factors have a common impact in the material: they are strongly correlated to the mobility on the molecular level. That is why a huge amount of work has been devoted to the study of translational/rotational mobility that occurs within the polymeric chains. This review is intended to provide a brief survey on such kinds of mobilities, how they can be studied and what are their main characteristics. Examples on systems studied in our groups will be provided, obtained by dielectric and mechanical spectroscopies and differential scanning calorimetry. It will be mainly focused on molecular motions that occur in the solid phase (i.e., to temperatures up to the rubbery plateau). The dynamics in blends or copolymers will be avoided here, as they would deserve a special discussion in their own context. Special attention will be paid to the glass transition and the mobility that occurs below and above it. The dynamics that are observed in peculiar systems, such as semi-crystalline or liquid crystalline polymers, will be addressed.