Recent advances in the photometric investigation of classical pulsators with the Kepler/K2 and TESS missions

Nearly continuous, densely sampled, space-based photometry allows us to recover the finest details in the light variations of stars. The number of such light curves have been increasing rapidly in the last few years thanks to the extended mission of the Kepler space telescope and the launch of the TESS mission. This new era brings us new perspectives in RR Lyrae and Cepheid studies, where low amplitude phenomena can be studied in a wide range of individual stars and on a statistical basis. In this proceedings I review the recent investigations of the Kepler, K2 and TESS fields, as well as the challenges in accurately reducing high-quality photometry.