Awaji Island (淡路島 Awajishima) is a not-terribly-large island - about the same size as Singapore - that marks the eastern boundary of the Seto Inland Sea of Japan. Thanks to a set of new bridges and a cross-island expressway, most visitors just zip through on their way from Honshu to Shikoku.
Awajishima has some claim to being the oldest settled area in Japan; the Kojiki mentions it under the name "Onokoroshima" and burial mounds (kofun) dating back thousands of years have been found on the island. The ningyo joruri puppet theater, which has evolved into bunraku, seems to originate from Awajishima.
Awajishima made a highly unusual but brief appearance on the world stage as the epicenter of the Great Hanshin Earthquake of 1995 that killed over 6000 people. However, Awajishima was (and remains) far less built up than the suburbs of Kobe across the bay, which took the brunt of the damage. It was also the island where the England soccer team stayed during the World Cup in 2002.
The southern tip lies a mere kilometer off the coast of Shikoku, and a bridge now straddles the Naruto Strait, famed for the whirlpools that form as the tide flows in and out. The very name "Awaji" means "road to Awa", the former name of current Shikoku prefecture of Tokushima.
At the other end of the island, some 50 kilometers away, the northern tip is not far from the port city of Kobe on Honshu, and the immense 3.5 km Akashi Kaikyo Bridge — the world's longest — now connects Awaji to the mainland. Politically (and in geographic terms somewhat oddly), despite its proximity to Shikoku, Awaji is a part of Honshu's Hyogo prefecture.
Highway buses connect Kobe Airport and Sumoto four times daily (two hours, ¥2000).
A highspeed ferry used to run between Sumoto and Kansai International Airport but this service stopped in 2007.
The inter-island expressway will get you from Akashi to Naruto, but it isn't advised unless you're willing to part with ¥5000 in tolls. Furthermore, signage is in Japanese and may be incomprehensible to a foreigner.
There are no direct train services to Awaji Island. Highway buses run directly from major train stations, such as Shin-Kobe on the shinkansen (¥1800 to Sumoto), and Osaka and Sannomiya stations on the regular JR line (¥2300 and ¥1800 to Sumoto, respectively). From Shin-Osaka station you must either take a local train one stop to Osaka station, or remain on the shinkansen to Shin-Kobe, to transfer to the bus.
Buses to Awaji Island are not valid with the Japan Rail Pass. Tickets can be purchased from "Midori-no-Madoguchi" locations at each station.
Even cheaper and more scenic, but available for the northern crossing only, are ferries that cross from Akashi to Iwaya for ¥450 (13 minutes) via the Jenova Line  located south of JR Akashi Station.
Public transport is limited to very occasional buses. Awaji Kotsu posts the bus schedule (only available in Japanese). Unusually for Japan, there are no trains on the island. If you don't have your own set of wheels, hitchhiking is a viable option.
Check out the beaches, especially on the more sparsely settled northern coast. They're a popular nearby summer getaway for Kansai-ites. There are also a number of hot springs (onsen), the best known of which are Awaji's largest town Sumoto and the mildly radioactive(!) waters of Iwaya adjacent to the northern bridge.
Ttoday's Awajishima is known primarily for its bridges and onions. The current total population hovers around 150,000, and (unlike most rural areas in Japan) is slowly on the rise due to the improved connections to the mainland. Scattered here and there are a number of herb and biwa (loquat) farms. The southern coast has a hideous but huge concrete statue of the Buddhist deity Kannon and the inevitable Onokoro Amusement Park.
1 Akashi Kaikyo Bridge (明石海峡大橋) (Take JR Kobe Line and get off at Maiko Station.). Completed in 1998, this majestic bridge dwarfs the village of Iwaya below. The bridge's total length is 3,991 meters, and the main span's length of 1,991m makes it the longest suspension bridge in the world. The bridge is attractively lit at night.
Naruto Whirlpools. See the whirlpools, either at the rest area on the expressway near Onaruto Bridge or by cruise.
Awaji is famous for their onions, fish and cheese.
Awaji has a scattering of ryokan and minshuku, concentrated in the hot spring areas. There are also a number of campsites, especially on the less populated western coast.