In recent years, some evidence has emerged of temporal and also spatial variations of the fine-structure constant, on cosmological scales and at a fractional level of a few parts per million. To test these claims we are conducting a Large Program with the VLT UVES. We are obtaining high-resolution (R~60000 and high signal-to-noise ratio (S/N~100) UVES spectra calibrated specifically for this purpose. I will present some of the early results of this program, but I will also discuss some classes of models where such variations arise, and prospects for more stringent constraints with future facilities.

Place: Physics Dept. Meeting Room, 2th floor, IST