The radial-velocity (RV) method is one of the most successful in the detection of exoplanets, but is hindered by the intrinsic RV variations of the star, which can easily mimic or hide true planetary signals. kima is a package for the detection and characterization of exoplanets using RV data. It fits a sum of Keplerian curves to a timeseries of RV measurements and calculates the evidence for models with a fixed number Np of Keplerian signals, or after marginalising over Np. Moreover, kima can use a GP with a quasi-periodic kernel as a noise model, to deal with activity-induced signals. The hyperparameters of the GP are inferred together with the orbital parameters. The code is written in C++, but includes a helper Python package, pykima, which facilitates the analysis of the results.