  Long-period variables are bright, evolved red giant stars showing periodic
photometric changes due to stellar pulsation. They follow one or more
period-luminosity and period-age relations, which make them highly promising
distance indicators and tracers of young and intermediate-age stellar
populations. Such a potential is especially interesting in view of the massive
amount of data delivered by modern large-scale variability surveys. Crucially,
these applications require a clear theoretical understanding of pulsation
physics in connection with stellar evolution. Here, I describe an ongoing
effort from our collaboration dedicated to the modelling of stellar pulsation
in evolved stars, and how this work is impacting our capability of
investigating long-period variables and exploiting them for other astrophysical
studies. Furthermore, I present our ongoing work aimed at assessing the
potential of semi-regular variables, an often neglected sub-type of long-period
variables, to be distance indicators complementary to their better-known, more
evolved counterparts, the Mira variables.
