High-precision space photometry of classical pulsating stars: lessons learned and future potentials

Nearly all space-based, time-series photometry missions observed classical pulsators. The extensive and high-precision data revealed a treasure trove of new information, from a diversity of mode content to dynamical phenomena or even precise parallaxes. In this talk I present some of the highlights that came from time series photometry and the prospects they offer, with particular emphasis on the possibility to determine seismic masses of RR Lyrae stars. With the help of K2 photometry of the nearest globular cluster, M4, we have been able to (almost) directly compare RR Lyrae masses to their co-eval red HB counterparts based on more than just evolutionary considerations, presenting a new test for stellar modeling. But there is still a lot to be done and to be learned from the existing observations, especially from the TESS mission. I review some of the open questions from TESS, as well as the potential of the PLATO, Roman and Earth2.0 space telescopes, which will expand our knowledge on pulsating stars even further towards the end of the decade.