Red supergiants (RSGs) are the brightest stars in the near-infrared. The existence of their period-luminosity relation (PLR) will be very helpful in determining cosmological distances. This review discusses the development in identification of RSGs, calculation of their light variation period, determination of the PLR, and the uncertainties associated. It is found that the PLR of RSGs exhibits the smallest scatter in the near-infrared, in particular within the P – MK relation. The PLRs in the LMC, SMC, M31, and M33 show no obvious dependence on the galactic metallicity, which follows approximately the relation as MK ≈ −3.1 log P – 1.9.

We performed a deep Hi and Hα mapping of M31 and M33 in order to get accurate kinematical data of those two galaxies and also to make a comparison between the Hi and Hα kinematics. The Hi data were obtained with the DRAO interferometer and the Hα data with the Fabry-Perot system of the Observatoire du mont Mégantic using an EMCCD as a detector. These data will give us the best possible datasets to derive accurate rotation curves and mass models for those two Local Group spirals and provide some new data for the Hii regions studies of these galaxies. While the Hi observations are of low resolution (~1 arcmin), the high resolution of the Hα data (~1 arcsec) should allow us to get much more details in the central regions, allowing at the same time a much better determination of the kinematical parameters. Hence, the inner part of the rotation curve, so inportant to constraint properly the mass models, will be determined more accurately.