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.

We derive and compare kinematic parameters of the Galaxy using the PMA and Gaia TGAS data. Two methods are used in calculations: evaluation of the Ogorodnikov-Milne model (OMM) parameters by the least square method (LSM) and a decomposition on a set of vector spherical harmonics (VSH). We trace dependencies on the distance of the derived parameters including the Oort constants A and B and the rotational velocity of the Galaxy Vrot at the Solar distance for the common sample of stars of mixed spectral composition of the PMA and TGAS catalogues. The distances were obtained from the TGAS parallaxes or from reduced proper motions for fainter stars.

The A, B and Vrot parameters derived from proper motions of both catalogues used show identical behaviour but the values are systematically shifted by about 0.5 mas/yr.

The Oort B parameter derived from the PMA sample of red giants shows gradual decrease with increasing the distance while the Oort A has a minimum at about 2 kpc and then gradually increases.

As for models chosen for calculations, first, we confirm conclusions of other authors about the existence of extra-model harmonics in the stellar velocity field. Secondly, not all parameters of the OMM are statistically significant, and the set of parameters depends on the stellar sample used.

We present the Three-mm Ultimate Mopra Milky Way Survey, a new mm-wave molecular-line mapping survey of the southern Galactic Plane, and its first data releases and science results. ThrUMMS maps a 60° × 2° sector of our Galaxy's fourth quadrant, using a combination of fast mapping techniques with the Mopra radio telescope, simultaneously in the J = 1→0 lines of 12CO, 13CO, C18O, and CN near 112 GHz, at 1′.2 and 0.3 km s−1 resolution, with 1.2 K/ch sensitivity for 12CO and 0.7 K/ch for the other transitions. The calibrated data cubes from these observations are made freely available to the community on the ThrUMMS website, http://www.astro.ufl.edu/thrumms, after processing through our pipeline. Here, we summarise the first science results, on global variations in the iso-CO line ratios and on a detailed multiwavelength study of the GMCs near l=333°.

Very recently, a number of obscured massive open clusters have been identified in the Milky Way. A very significant fraction of them lie either close to the base of the Scutum Arm or towards Galactic longitude of 350°. We are studying these clusters and their neighbourhoods, finding very good evidence for a major starburst region close to the near tip of the Galactic Long Bar.

Variable stars have a unique part to play in Galactic astronomy. Among the most important of these variables are the Cepheids (types I and II), the RR Lyraes and the Miras (O- and C-rich). The current status of the basic calibration of these stars in their roles as distance, structure and population indicators is outlined and some examples of recent applications of these stars to Galactic and extragalactic problems are reviewed. The expected impact of Gaia on this type of work is discussed and the need for complementary ground based observations, particularly large scale near-infrared photometry, is stressed.

Due to their compactness, persistence and slow motion, Class II CH3OH masers are excellent targets for parallax and proper motion measurements for massive star-forming regions in the Galactic Disk. These measurements can be used to improve our understanding of the spiral structure and dynamics of the Milky Way. At the same time, Class II CH3OH masers can also be used to study gas kinematics close to the exciting star, tracing rotation, infall and/or outflow motions.

We show that anomalous extinction (deviations from the traditionally adopted RV = AV/E(B − V) = 3.1 introduces large uncertainties in the distances of stars, for distances larger than 1-2 kpc. We argue that for such distances and for directions close to the galactic plane, the use of extinction models based on the gas distribution in the Galaxy is safer, for the moment, than the use of extinction maps.

Deep recent surveys have considerably improved our picture of the outer Galactic halo by unveiling a complex level of substructuring in the form of streams, stellar clouds and debris systems. Here I discuss some of the recent findings and present their general properties.

Astrometric observations with the VLBA with accuracies approaching ~ 10 μas are being conducted in order to better understand the Galaxy. The location of Sgr A* on infrared images can be determined with an accuracy of a few mas, using stars with SiO maser emission as a calibration grid for infrared images. The apparent proper motion of Sgr A*, which is dominated by the effects of the orbit of the Sun around the Galactic center, has been measured with high accuracy. This measurement strongly constrains Θ0R0 and offers a dynamical definition of the Galactic plane with Sgr A* at its origin. The intrinsic motion of Sgr A* is very small and comparable to that expected for a supermassive black hole. When combined with infrared results, this provides overwhelming evidence that Sgr A* is a supermassive black hole. Finally, we are engaged in a large project to map the spiral structure and kinematics of the Galaxy. Preliminary trigonometric parallaxes, obtained with the VLBA, to eight massive star forming regions are presented.