  Research in extrasolar-planet science is data-driven. With the advent of
radial-velocity instruments like HARPS and HARPS-N, and transit space missions
like Kepler, our ability to discover and characterise extrasolar planets is no
longer limited by instrumental precision but by our ability to model the data
accurately. This chapter presents the models that describe radial-velocity
measurements and transit light curves. I begin by deriving the solution of the
two-body problem and from there, the equations describing the radial velocity
of a planet-host star and the distance between star and planet centres,
necessary to model transit light curves. Stochastic models are then presented
and I delineate how they are used to model complex physical phenomena affecting
the exoplanet data sets, such as stellar activity. Finally, I give a brief
overview of the processes of Bayesian inference, focussing on the construction
of likelihood functions and prior probability distributions. In particular, I
describe different methods to specify ignorance priors.
