If you've every tapped more then a few holes in either steel or aluminum then you've probably broken a tap off in the material. Now what?
Here's a solution that I've been working with for a couple of years now and no tap has beat me yet.
First pic, broke the tap off in a piece of steel. This can really ruin your day..
If you are proficient with a TIG welder then you slowly start adding a bit of metal to the piece of broken off tap. Add a bit more until you have a little nub sticking up above the surface.
Next, Drop a nut (in this case a 1/4- 20) over the nub. Weld the nub to the nut.
While the nut is still warm use a wrench to slowly rock the nut back and fourth a bit at a time.
Success! After a little patience you can just walk the busted tap out of the hole and you are golden!
I hope this is as valuable to others as it has been to me.
Post back if you try this and let us know your results.