A liquid is said to become glass when cooled to a temperature T infinitesimally below the temperature Tl→g. According to the glass-formation criteria, either, (I) τs=CI/qc at Tl→g, or, (II) (dτs/dT) ≅ CII/qc, or, (III) (τs/T)≅CIII/qc, where τs is taken as equal to τα, the relaxation time of the α-process, qc is the cooling rate, and CI=16.67K, CII≅1, and CIII≅1. Criterion I is generally used in glass phenomenology, criterion II was related to the effective enthalpy of activation in the Tl→g range and recommended over criterion I, and criterion III was used for discussing the pressure dependence of Tl→g. We investigate their merits by comparing formally the criteria-based τs at Tl→g in an ideal case against τα at T=Tl→g, and discuss the effects of using the glass-liquid transition temperature, Tg→l, the fictive temperature, Tf, and the midpoint temperature of the Cp-T plots as alternatives to Tl→g. The three criteria yield basically different results. Moreover, Tl→g differs from the kinetic freezing temperature of the α-relaxation process, and CI varies with both qc and the material. We suggest that contributions from several properties of ultraviscous liquids affect the shape of the Cp-T scans from which Tl→g is determined. The findings have consequences for interpretations in which τs is used as τα.