There are frequent charter flights to Rhodes Island from many airports of Western and Eastern Europe and from the Middle East. EasyJet also operates a scheduled flight service from Gatwick.
If you prefer to fly from or change at a Greek Airport, there are many connections to Rhodes from Athens, Thessaloniki, Crete and from many other Greek islands, such as Mykonos, Santorini, Kos etc. (See Aegean Airlines, Olympic Airlines and Sky Express for details and booking). Cyprus Airways flies from Cyprus to Rhodes via Crete.
Rhodes is a major port with sea links not only to Athens, Crete, and the islands of the Aegean, but also to Cyprus, Turkey, and Israel.
In late spring and summer, there's daily hydrofoil or catamaran service from Mandraki Harbor to Kos, Tilos, Nissiros and Simi, and less predictable service to many destinations, including Kalimnos, Leros, Patmos, Kastellorizo, and Samos