Is there a specific type of doctor that handles rare diseases / conditions?

Specific specialists: Exist for the area of illness a given patient might have. For instance, if you have heart problems, then a cardiologist would be well-versed in routine as well as more esoteric rare cardiac illnesses. The same goes for infectious diseases, gi-tract issues, blood disorders (hematologist), etc. Match the disease/illness to the area of physician specialty. Universities may have more experience also.