Classical Cepheids: High-precision Velocimetry, Cluster Membership, and the Effect of Rotation

Classical Cepheids are crucial calibrators of the extragalactic distance scale. Despite the adjective 'classical' and their use as 'standard candles', many open problems remain and ensure a steady scientific interest in these objects. This thesis has contributed to the understanding of Cepheids via three different topics: (1) an unprecedented observational program dedicated to studying highly precise Doppler measurements (velocimetry), which as has enabled several observational discoveries; (2) a newly-developed astro-statistical method for conducting an all-sky census of Cepheids belonging to Galactic open clusters, which is suitable for the era of large surveys (big data) such as the ESA's Gaia space mission; (3) the first detailed investigation of the effect of rotation on populations of classical Cepheids using Geneva stellar evolution models, which provides an explanation for the 45-year old Cepheid mass discrepancy problem. Last, but not least, I investigated the implications of my work for the extragalactic distance scale