Weak gravitational lensing of distant galaxies by foreground structures has proven to be a powerful tool to study the mass distribution in the universe. Nowadays, attention has shifted from clusters of galaxies to the statistical properties of the large scale structures and the halos of (field) galaxies. These applications have become feasible with the advent of panoramic cameras on 4m class telescopes. In this review we will give an overview of recent advances in this fast evolving field of astronomy. We start with a discussion of the recent measurements of weak lensing by large scale structure (``cosmic shear''), which can be used to constrain cosmological parameters. We also show how weak lensing can be used to measure the relation between galaxies and dark matter (galaxy biasing) directly. Another area that benefitted greatly from the current data is the weak lensing by galaxies (galaxy-galaxy lensing). Weak lensing provides a unique probe of the gravitational potential on large scales. Hence, in the context of dark matter, it can provide constrains on the extent and shapes of dark matter halos. Furthermore, it can test alternative theories of gravity (without dark matter). The best constraint comes from the first detection of the anisotropy of the lensing signal around lens galaxies, which suggest that the dark matter halos are flattened. An isotropic signal, as predicted by MOND, is excluded with 99% confidence.

submitted to NewA Reviews, based on review given at workshop on MOND, paris, October 4 and 5, 2001