Local Group galaxies, particularly the Large and Small Magellanic Clouds, have historically played and continue to play a unique role in studies of the period–luminosity (PL), period–luminosity–color (PLC), and period–Wesenheit (PW) relations, not just for pulsating stars. In recent years, significant efforts have been devoted to calibrate the PL, PLC, and PW relationships at different wavelengths, including studies of the influence of metallicity and nonlinearities on the accuracy of measured distances. However, the PL diagram has many more astrophysical applications. It serves as a vital tool for classifying different types of pulsating stars and can even facilitate the discovery of new classes of variable stars. Moreover, it aids in distinguishing among various modes of pulsation, facilitates the identification of pulsating stars that are members of binary systems, and enables studies of the three-dimensional structures of neighboring galaxies. In this contribution, I present the latest results on the PL, PLC, and PW relations obeyed by various types of variable stars in Local Group galaxies – from δ Scuti stars to Mira variabless and from close binary systems to the mysterious long secondary periods exhibited by red giant and supergiant stars.

Cepheids and RR Lyrae stars are important pulsating variable stars in distance scale work because they serve as standard candles. Cepheids follow well-defined period-luminosity (PL) relations defined for bands extending from optical to mid-infrared (MIR). On the other hand, RR Lyrae stars also exhibit PL relations in the near-infrared and MIR wavelengths. In this article, we review some of the recent developments and calibrations of PL relations for Cepheids and RR Lyrae stars. For Cepheids, we discuss the calibration of PL relations via the Galactic and the Large Magellanic Cloud routes. For RR Lyrae stars, we summarize some recent work in developing the MIR PL relations.

Cosmological models predict that large galaxies like the Milky Way formed from the accretion of smaller stellar systems. The most spectacular of these merger events are stellar tidal streams, rivers of stars and dark matter that envelop the discs of spiral galaxies. We present a research project for a collaboration with amateur astronomers in the study of the formation process of our Galaxy. The main objective is the search for RR Lyrae variable stars in the known stellar streams (Sagitarius, Monoceros, Orphan, etc) a project that can be carried out using small telescopes. The catalogue of candidate variable stars were selected from SDSS data based in colour criteria and it will be sent to interested amateur astronomers who wish to participate in scientific research in one of the most active and competitive topics in Galactic astronomy.