Pulsating stars play a crucial role in the calibration of the cosmic distance scale as well as in tracing the properties of the associated stellar populations. In the era of large observational surveys and precise astrometric missions, it is crucial to rely on accurate stellar pulsation models able to predict the observed behaviors for different physical assumptions. Indeed, the relations currently used in the literature to derive individual and mean distances of mainly radially pulsating stars such as Cepheids and RR Lyrae are well physically understood, but are also known to depend on a number of often unknown parameters. Recent extensive sets of stellar pulsation models developed by various authors show how variations in the physical assumptions can affect the theoretical prediction of the instability strip boundaries, the morphology and amplitude of light and radial velocity curves, and the consequent Period-Luminosity, Period-Luminosity-Color and Period-Wesenheit relations. These aspects are discussed in the framework of current open problems in the field of classical pulsating stars.
