If I have an exclusive license, can I sue for infringement?

The answer depends on the terms of your license agreement. Every license agreement conveys a part of the owner's "bundle of rights". (For example: the owner of a photography can license that work to be used online to one party and license reproduction in hard copy form to another party). A license can be all rights or just a small portion. 

The Copyright owner can reserve the right, in full, to file suit against a potential infringement on the work. This is part of the bundle of rights that can be conveyed in a license agreement.  Failure to address this issue in the  agreement can cause a potential dispute between the owner and licensee if a suit is filed.

A non-exclusive licensee would likely never be able to file suit for infringement.  But the extent of a license is not always as clear as the title of the agreement may suggest.