Yes. Our laser welder allows us to repair virtually any metal eyeglass frames... including titanium. (We flood the laser's chamber with Argon gas to provide an oxygen free barrier, which is necessary for a good weld on titanium). It repairs breaks in metal eyeglass frames without damaging the metal plating or the coating. The bond is 60 times stronger than a solder weld and is nearly invisible to the naked eye. Almost always, we will try to do these repairs while you wait.
As for plastic frames. Yes, we work on them too.
Limitation:
The one area of eyeglass repair we have had difficulty with(along with everyone else) is when the break is inside the temple hinge spring. Generally, we can put them back together, but it's not a perfect solution, as we either have to "freeze" the two pieces together (you won't be able to fold them) or we can often fuse the two pieces together, but they won't have the "spring" allowing them to grip your head.
Word of caution:
If you try to fix your eyeglass frame with lead solder or a jewelers torch, you run the risk of weakening your frame with the intense heat. If you apply super glue or epoxy to your frame, you run the risk of contaminating the metal and finish on your eyeglasses. Additionally, lasers are ineffective on areas coated with glue.