Santorini is the last of the Cyclades islands to the South. The closests islands are Ios, Folegandros, Sikinos to the North, Anafi and Amorgos to the East and Crete to the South.
We refer to it as one, but actually is a complex of five islands. Santorini (Thira) is the main island and around it Thirasia and Aspronisi (parts of the ancient Stroggili) and the two volcanic islands Palea Kameni and Nea Kameni.
It was one island named Stroggili (circle in Greek) until about 1645 BC, when the volcano in the middle of the island erupted and Caldera was created. The two volcanic islands appeared much later from various eruptions starting 157 BC and the last one to be in the 20th century (1950).
Many reasons made this island famous worldwide and more or less we all have seen a picture of it (it was that picture the travel agency used for Greece). There is a talk about the connection between Thira and mythical Atlantis.
Also Jules Verne made Santorini famous with its books "Twenty Thousand Leagues Under the Sea" and "The mysterious island" where captain Nemo and his crew watch the volcano eruption. He was one of the visitors and scientists that came to Thira during the eruptions of 1866 - 1870 and wrote the well known book just after it. It is realy the mysterious island, the volcano rules, the caldera view is the most breathtaking one on the planet!
If you are after the caldera view have a look at Fira, Oia, Imerovigli, Firostefani, Akrotiri. For the best beaches check Perissa, Kamari, Perivolos, Vlihada and Red beach.
Santorini is connected to Piraeus, Thessaloniki, Crete, Rhodes, Kos and all the major Cyclades islands (Mykonos, Paros, Naxos, Sifnos, Milos, Tinos, Syros) by boat and Athens and many countries direct by plane.