Abstract
Cepheids and RR Lyrae are among the most important primary distance indicators to calibrate the extragalactic distance ladder and excellent stellar population tracers, for Population I and Population II, respectively. In this paper I first mention some recent theoretical studies of Cepheids and RR Lyrae obtained with different theoretical tools. Then I focus the attention on new results based on nonlinear convective pulsation models in the context of some international projects, including VMC@VISTA and the Gaia collaboration. The open problems for both Cepheids and RR Lyrae are briefly discussed together with some challenging future application.
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