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.