Mk1 Golf GTI - Can I swap in a later engine?

Considering swapping out the MK1 Golf GTI's original 1.8L engine for a later version, perhaps a 2.0L or 2.1L unit, to gain more power and modernize the car. What are the feasibility and potential issues with this swap? Has anyone done it successfully, or is there a better way to breathe new life into my classic GTI?