Methods and apparatus for separating substrates are disclosed, as are articles formed from the separated substrates. A method of separating a substrate having first and second surfaces includes directing a beam of laser light to pass through the first surface and, thereafter, to pass through the second surface. The beam of laser light has a beam waist located at a surface of the substrate or outside the substrate. Relative motion between the beam of laser light and the substrate is caused to scan a spot on a surface of the substrate to be scanned along a guide path. Portions of the substrate illuminated within the spot absorb light within the beam of laser light so that the substrate can be separated along the guide path.