Astrophysical applications of gravitational microlensing

Since the first discovery of microlensing events nearly two decades ago, gravitational microlensing has accumulated tens of TBytes of data and developed into a powerful astrophysical technique with diverse applications. The review starts with a theoretical overview of the field and then proceeds to discuss the scientific highlights. ( 1) Microlensing observations toward the Magellanic Clouds rule out the Milky Way halo being dominated by MAssive Compact Halo Objects (MACHOs). This confirms most dark matter is non-baryonic, consistent with other observations. (2) Microlensing has discovered about 20 extrasolar planets (16 published), including the first two Jupiter-Saturn like systems and the only five cold Neptunes yet detected. They probe a different part of the parameter space and will likely provide the most stringent test of core accretion theory of planet formation. (3) Microlensing provides a unique way to measure the mass of isolated stars, including brown dwarfs and normal stars. Half a dozen or so stellar mass black hole candidates have also been proposed. (4) High-resolution, target-of-opportunity spectra of highly-magnified dwarf stars provide intriguing age determinations which may either hint at enhanced helium enrichment or unusual bulge formation theories. (5) Microlensing also measured limb-darkening profiles for close to ten giant stars, which challenges stellar atmosphere models. (6) Data from surveys also provide strong constraints on the geometry and kinematics of the Milky Way bar (through proper motions); the latter indicates predictions from current models appear to be too anisotropic compared with observations. The future of microlensing is bright given the new capabilities of current surveys and forthcoming new telescope networks from the ground and from space. Some open issues in the field are identified and briefly discussed.