Gravitational microlensing of light occurs when the gravity of a star bends the light coming from a more distant star. The distant star temporarily appears brighter due the light being focused by the gravity of the nearer star2.
Astrometry method of detection requires measuring the stars position in the sky in relation to other stars and observing how the position changes overtime. If the star has a planet orbiting it then the gravitational pull of the planet will cause the star to wobble and as a result its position in space will change2.
The Transit and Radial velocity methods have been the two most successful methods for detecting exoplanets.
By far the greatest number of planets found is by using the Transit method, 3126 planets2. Valuable information can be deduced from this method of detection such as the planets atmospheric composition as well as temperature. As the planet transits the parent star, some of the starlight passes through the planet’s atmosphere. Detecting and analyzing this light can lead to information about the planet’s composition e.g. water vapor, methane etc2.