Any material possessing a wide relaxation time spectrum which is a strong function of temperature will exhibit a glass transition as the mean relaxation time crosses the time scale of observation; for example, the metastable supercooled liquid freezes into a glass state. After a review of calorimetric investigation and characterization of the glassy state, the fictive temperature concept is recommended for the assignment of glass transition temperature. The glass transition temperature (Tg) is defined as the intersecting temperature of extensive thermodynamic properties (such as enthalpy, entropy, and volume) extrapolated from temperatures above and below Tg toward the Tg. This assignment of Tg is dependent only on the conditions of glass formation and is independent of the rate of observation. Therefore, the Tg so defined may be considered as a property of the glass, free of observational artifacts. The width of the glass transition is often 30 to 50 K; therefore, a description of the width and the intensity of the transition would be helpful. By slow cooling or annealing, not only a relaxation peak shows up, but the transition also appears sharper as the width narrows to about 10 K. A continuous slow cooling procedure is preferred over the annealing procedure to locate weak glass transitions, as annealing may produce more than one relaxation peak for exceptionally wide glass transitions. For glass transitions even harder to locate, Tg may be bracketed by using the relaxation nature of the glass, by observing spontaneous exothermic adiabatic temperature drifts of quenched glasses and endothermic drifts of slow-cooled or annealed glasses.