This talk presents the crucial role that type-I Cepheid variable stars play in improving the understanding of how stars and the cosmos evolve. Starting from the recently reported Hubble constant tension that may imply a need for new physics beyond standard cosmology, I will describe ongoing efforts to measure H0 with an accuracy of 1%. Specifically, I will present an ongoing large observing program operating on both hemispheres that has measured more than 15,000 high-precision radial velocities of Cepheids in support of accurate parallaxes and alternative distance estimates based on Baade-Wesselink-type methods. Highlighting the impact of binaries for accurate parallax determination, I will show that stars physically associated with Cepheids contribute a modest photometric bias of less than 0.23% to H0, which may be further reduced in the future. The second part of the talk presents how rotation is expected to impact the evolutionary paths of Cepheids and how this relates to their use as cosmic yardsticks. Time permitting, I will present the curious case of Polaris, our nearest Cepheid, whose Gaia-based luminosity estimate and multi-periodic variability seem to defy theory, thus underlining the urgent need for a more detailed astrophysical understanding of our most important standard candles.