Classical Cepheids are key astrophysical laboratories, providing fundamental constraints on stellar pulsation, binary evolution, and Galactic and extragalactic structure and cosmology. Their radial velocities contain rich physical information and are usually dominated by large-amplitude stable pulsational motion. However, other effects, such as orbital motion for binary system and departures from a strictly stationary pulsation, introduce detectable variations that complicates their interpretation. Disentangling these contributions requires long temporal baselines, high measurement precision, and homogeneous analysis methods. This thesis presents a comprehensive study of Cepheid radial-velocity variability based on the VELOCE (VELOcities of CEpheids) project, an observational program designed to obtain high-precision radial velocities of Galactic Cepheids. Using more than a decade of spectroscopic observations, this work characterizes Cepheid pulsational radial-velocity curves with unprecedented precision, systematically identifies and models spectroscopic binaries, and detects and characterizes additional spectroscopic variability beyond strictly periodic pulsation. Particular attention was given to devising a modeling strategy that determines a highly precise pulsation radial-velocity curve, enabling orbital motion and additional variability to be identified through residual analysis within a homogeneous framework. Beyond the analysis of individual stars, this thesis addresses the challenge of extending high-precision, targeted studies to the era of large spectroscopic surveys, where Cepheids are typically observed for only a few epochs. A Bayesian framework is developed to reconstruct Cepheid radial-velocity curves from sparse data by leveraging the information encoded in the VELOCE dataset. This approach enables the inference of systemic velocities, amplitudes, and binary diagnostics with quantified uncertainties, even in regimes where dense phase coverage is unavailable. Together, the results presented in this thesis establish Cepheid radial velocities as a rich, multi-component time-domain observable and provide new empirical constraints and methodological tools required to exploit Cepheid velocimetry for stellar physics and Galactic and extragalactic dynamics in current and future spectroscopic surveys.