Modern fishing poles are made from composite materials- typically fiberglass and carbon fiber. Like other materials, they can be broken when they are overloaded. Age and stress weaken the material over time, and the weakest point will eventually break.
Like many other composite materials, they can be repaired with the proper techniques and materials. Youtube user Northwest Ontario Fishing demonstrates this below.
As always, proper surface preparation and the use of compatible repair materials will help to ensure a successful outcome.