  Exoplanets can be detected with various observational techniques. Among them,
radial velocity (RV) has the key advantages of revealing the architecture of
planetary systems and measuring planetary mass and orbital eccentricities. RV
observations are poised to play a key role in the detection and
characterization of Earth twins. However, the detection of such small planets
is not yet possible due to very complex, temporally correlated instrumental and
astrophysical stochastic signals. Furthermore, exploring the large parameter
space of RV models exhaustively and efficiently presents difficulties. In this
review, we frame RV data analysis as a problem of detection and parameter
estimation in unevenly sampled, multivariate time series. The objective of this
review is two-fold: to introduce the motivation, methodological challenges, and
numerical challenges of RV data analysis to nonspecialists, and to unify the
existing advanced approaches in order to identify areas for improvement.
