This chapter describes sub-Tg transitions in amorphous and semicrystalline polymers. The results of dynamic mechanical and dielectric measurements of important amorphous and semicrystalline polymers are summarized and conclusions regarding the origin of sub-Tg molecular motions are offered. Temperature assignments for principal relaxations are the temperatures at the maximum of the dynamic-mechanical or dielectric tan δ or loss modulus peaks at the reported frequencies. Values determined from tan γ data are slightly higher than those determined from loss modulus values, and temperature assignments increase with increasing frequency. Typically, peak assignments for glass-transition temperature (Tg) are slightly higher (ca. 15–20 ºC) than obtained by dilatometry at low cooling rates. Where available data for only dry, unconditioned samples are reported. The prevailing view is that the glass transition (α relaxation in amorphous polymers) is associated with the coordinated motion of 50-100 carbon atoms and associated substituent groups about a chain axis, while secondary relaxations reflect the motions of smaller numbers of carbon atoms about the chain axis (e.g., crankshaft-type motions) or motions of substituent groups. The dynamic-mechanical and dielectric spectra of semicrystalline polymers are more complex than those of amorphous ones. This complexity results from the presence of additional transitions resulting from crystalline regions, varying degrees of crystallinity in different samples, and the possibility of different crystalline forms. Glass-transition and secondary-relaxation temperatures of amorphous polymers and semicrystalline polymers are tabulated.