  The relationship between the integrated H$\beta$ line luminosity and the
velocity dispersion of the ionized gas of HII galaxies and giant HII regions
represents an exciting standard candle that presently can be used up to
redshifts $z\sim~4$. Locally it is used to obtain precise measurements of the
Hubble constant by combining the slope of the relation obtained from nearby
($z<0.2$) HII galaxies with the zero point determined from giant HII regions
belonging to an `anchor sample' of galaxies for which accurate
redshift-independent distance moduli are available (e.g Cepheids, TRGBs).
Through this chapter, we present a general description of the method and
results obtained so far in the determination of the local value of the Hubble
constant and cosmological constraints. We account for the main systematic
effects associated with the method and the possibility of improvement in the
future. The discussion presented here is the product of an independent approach
to the standard methods used in the literature to measure distances and,
although at present less precise than the latest SNIa results, it is amenable
to substantial improvement.

Cosmology and Nongalactic Astrophysics