The discovery of ferroelectric barium titanate (BaTiO$_3$) in 1942 began the present era of dielectrics-based electronic ceramics. Ferroelectric barium titanate has a high dielectric constant and after the recognition of BaTiO$_3$ as a new ferroelectric compound, various attractive electrical properties have been extensively studied and reported. Since then, pioneering work on valence-compensated semiconduction led to the discovery of the positive temperature coefficient (PTC) of the resistance effect found in doped BaTiO$_3$. Significant progress has since followed with respect to understanding the PTC phenomena, advancing materials capabilities, and developing devices for sensor and switching applications. In this paper, the theoretical aspects of the various PTC models are discussed and the future trends of practical applications for PTC devices are briefly mentioned.