In the last five years, the number of periodic variable stars has increased by two million. We used the ZTF DR2 data to find and build a catalog that includes 780,000 periodic variable stars. These periodic variable stars were classified into 11 types, which greatly complemented the variable stars in Galactic disk. Based on the latest ZTF DR16 data, we found 2 million variable candidates. We trained a machine learner to classify variable stars, and the learner had a prediction accuracy of 94%. Using millions of variable stars, we carried out studies to optimize the period–luminosity relations and the Galactic structure and the extinction law. With the future China Space Station Telescope, millions of variable stars in the Local Group will be discovered. They help to study the structure of our Local Group and also to cross-check the distance ladders based on different variable stars.

RR Lyrae (RR Lyr) stars are a well-known and useful distance indicator for old stellar populations such as globular clusters and dwarf galaxies. Fundamental-mode RR Lyr (RRab) stars are commonly used to measure distances, and the accuracy of the determined distance is strongly constrained by metallicity. Here, we investigate the metallicity dependence in the period–luminosity (PL) relation of double-mode RR Lyr (RRd) stars. We find and establish a linear relation between metallicity and period or period ratio for RRd stars. This relation can predict the metallicity as accurately as the low-resolution spectra. Based on this relation, we establish a metallicity-independent PL relation for RRd stars. Combining the distance of the Large Magellanic Cloud and Gaia parallaxes, we calibrate the zero point of the derived PL relation to an error of 0.022 mag. Using RRd stars, we measure the distances of globular clusters and dwarf galaxies with an accuracy of 2-3% and 1-2%, respectively. In the future, RRd stars could anchor galaxy distances to an accuracy of 1.0% and become an independent distance ladder in the Local Group.