Weighted orbital integrals

This is an expanded version of a survey talk given at the Conference on Representations of Real Reductive Lie Groups, June 4 to June 8, 2006, at the Snowbird Mountain Resort, Utah. We explain the defi-nition of weighted orbital integrals and their Fourier transforms and report their known properties, leaving aside questions of endoscopy. We also announce some new results on those Fourier transforms over the reals