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.