Mykonos is connected year around with the world via Athens.
In summer every european airline operate to/from Mykonos with nonstop flights from major cities across the continent.
There are no longhaul flights to/from Mykonos with such a shhort runway. All longhaul flights must connect somewhere at major airports in Europe or Athens.
Athens International Airport has a wide offer connection to/from north America, Asia, Africa year around.
From Athens you can choose one of the many domestic flight to/from Mykonos operated by a selection of carriers.