The Role of Long Period Variable Stars in Observational Astrophysics

Long-period variables (LPVs) are evolved red giant and supergiant stars whose pulsations provide unique insights into late stages of stellar evolution and serve as essential tools in modern astrophysics. Their period-luminosity and period-age relations make them valuable distance and age indicators, while their light curve morphology, amplitudes, and multiperiodicity reveal the underlying physics of stellar interiors and mass-loss. In this review, we provide an overview of the current status of LPV studies, focusing on their observational properties and applications, including: - Modern classification of LPVs into Miras, semiregular variables (SRVs), and OGLE small-amplitude red giants (OSARGs), which occupy multiple period-luminosity sequences associated with different pulsation modes, chemical compositions, and evolutionary stages - Mira variables as reliable distance indicators across diverse stellar environments and their increasing role as standard candles - The increasing role of SRVs and OSARGs - Long secondary period (LSP) variables as potential tracers of exoplanets Together with advances in theoretical modeling, these developments establish LPVs as valuable tracers of Galactic structure, stellar populations, and the extragalactic distance scale.