  Since the first microlensing planet discovery in 2003, more than 200 planets
have been detected with gravitational microlensing, in addition to several
free-floating planet and black hole candidates. In this chapter the
microlensing theory is presented by introducing the numerical methods used to
solve binary and triple lens problems and how these lead to the
characterisation of the planetary systems. Then the microlensing planetary
detection efficiency is discussed, with an emphasis on cold planets beyond the
snow line. Furthermore, it will be explained how the planetary characterisation
can be facilitated when the microlensing light curves exhibit distortions due
to second order effects such as parallax, planetary orbital motion, and
extended source. These second order effects can be turned to our advantage, and
become useful to ultimately better characterise the planetary systems, but they
can also introduce degeneracies in the light curve models. It will be explained
how the use of modern observational and computational techniques enables
microlensers to solve these degeneracies and estimate the planetary system
parameters with very high accuracy. Then a review of the main discoveries to
date will be presented while exploring the recent statistical results from
high-cadence ground-based surveys and space-based observations, especially on
the planet mass function. Finally, future prospects are discussed, with the
expected advances from dedicated space missions, extending the planet
sensitivity range down to Mars mass.
