Nanoscale quasi-liquid intergranular films have been observed in various ceramic materials (Crit. Rev. Solid State Mater. Sci. 2007, 32:67), as well as in metals such as W-Ni (Acta Mater. 2007, 55:3131) and Mo-Ni (APL 2009, 94:251908). Several thermodynamic models are presented and discussed. First, using CALPHAD data, a premelting type model predicts onset grain boundary disordering at as low as 60-85% of the bulk eutectic/peritectic temperatures (APL 2008, 92:101902). This model quantitatively explains mysterious subsolidus activated sintering in refractory metals. Second, a systematical spectrum of interfacial phenomena, including prewetting/premelting, critical points, multilayer adsorption, layering/roughening, and complete wetting/drying, are predicted by combining diffuse-interface and lattice-gas models and incorporating colloidal type interfacial forces. This model also produces a series of grain boundary phases (complexions) with character similar to those observed by Dillon and Harmer. Finally, analogous phenomena at free surfaces and their thermodynamic models are reviewed (Annu. Rev. Mater. Res. 2008, 38:227).