Classical pulsating stars such as Cepheid and RR Lyrae variables exhibit well-defined Period–Luminosity relations at near-infrared wavelengths. Despite their extensive use as stellar standard candles, the effects of metallicity on Period–Luminosity relations for these pulsating variables, and in turn, on possible biases in distance determinations, are not well understood. We present ongoing efforts in determining accurate and precise metallicity coefficients of Period–Luminosity-Metallicity relations for classical pulsators at near-infrared wavelengths. For Cepheids, it is crucial to obtain a homogeneous sample of photometric light curves and high-resolution spectra for a wide range of metallicities to empirically determine metallicity coefficient and reconcile differences with the predictions of the theoretical models. For RR Lyrae variables, using their host globular clusters covering a wide range of metallicities, we determined the most precise metallicity coefficient at near-infrared wavelengths, which is in excellent agreement with the predictions of the horizontal branch evolution and stellar pulsation models.

Disentangling the structural components of the Milky Way requires knowledge of distances to various classes of objects, both young, which trace the Galactic disk, and old, which trace the Galactic bulge and halo. Variable stars that obey period-luminosity relations are perfect distance indicators for such studies. Here we discuss recent findings on the structure of our galaxy, inferred from period-luminosity relations for both young, old and intermediate-age variable stars, including Cepheids, RR Lyrae stars, δ Scuti stars, and long-period variables.

In this invited review I discuss the calibration and applications of the period–luminosity relation of classical Cepheid and RR Lyrae stars. After a brief introduction, starting with results from Hipparcos and discussing some post-Hipparcos era developments, I focus on recent results using Gaia Data Release 3 data. I present an overview of the most recent period–luminosity relations, a discussion and some new results on Cepheids in open clusters. I also discuss the effect of reddening and that the use of Wesenheit indices is actually an oversimplification to dealing with the problem of reddening.