Glass lenses are more durable and don't scratch as easily as easily as plastic, but can break if dropped or struck with a hard object. Plastic lenses are lighter and are available in more colors and coatings, but are more prone to deterioration from scratches. There's one plastic material, polycarbonate, which is ultra-impact resistant and is an excellent choice as a safety or sports lens. Polarized lenses effectively block reflected glare, a situation which occurs primarily near water or snow or off reflective surfaces nearby, such as car windows, metallic objects, etc. Light which strikes a horizontal reflective surface is reflected back into your eyes.
Polarized lenses are available in glass and plastics.
Glass lenses are usually a laminate of two pieces of glass with a plastic polarizing sheet sandwiched in between. A new product recently introduced has the polarizing layer cast inside the glass and is one solid lens. This makes for a lighter product and one which doesn't de-laminate over time. Plastic lenses are lighter than their glass counterparts and are sometimes made as a single laminate and sometimes are cast as above. They lighten to nearly clear when not in direct sunlight.