The musical form ska grew out of Jamaica in the early 1960s. Despite popular opinion, it actually came before reggae, not after. Credit for the creation of ska is given to many different people, but mention must be made of Clement "Sir Coxsone" Dodd, The Skatalites and Prince Buster. Lots of other people were there, and I'm sure by naming anybody at all, I'm going to leave somebody out. Most ska bands started out as a horn band, often just a bunch of studio musicians, with a rhythm section (guitar, bass, drums) backing up the horns. Vocals weren't always present, and vocalists were often separate performers from the band. In this, first wave ska shares a lot with jazz, one of its primary influences. For example, Duke Ellington had a band, but any number of vocalists could be singing in front of the band, or nobody could be singing at all. A lot of first wave ska bands acted the same way. A notable exception is Toots and the Maytals, considered by many to be the father of vocal ska. Due to the rising prominence of reggae in Jamaica and other factors, the first wave of ska ended by 1970, with labels either going out of business, bands breaking up, or former ska bands becoming reggae bands.
Notable first wave ska bands:
Second wave ska was an offshoot of the first wave, but with a lot of New Wave influence. Most of the bands in the second wave were British in origin, such as The Specials and Madness. Immigrants from Jamaica after that island gained its independence brought the island sound back to the UK. The New Wave influence on these bands resulted in a sound that was less horn based than first wave ska. More guitar was present in the sound, as well as increased vocals and keyboards and such. Hey, it was the 80s, they threw in all kinds of instruments, most of which weren't a good idea. The second wave of ska never really hit it huge in America. It was mostly popular in the UK and somewhat in Europe. This was partially because the primary driving force between the second wave of ska was Two Tone Records, formed in the UK in 1979 by Jerry Dammers. Two Tone had a unique image. The label promoted an end to racism and used an extensive black-white color combination in their image. The Two-Tone logo, of the man in the black suit, black hat, white shirt, white socks, and black shoes, was based on the rude boy scene back in Jamaica. Bonus points if you know his name. He was based on a picture of Peter Tosh of the Wailers. Sadly, Two-Tone went bankrupt in 1985 and the second wave of ska died shortly thereafter.
Notable second wave bands:
Third wave ska is the latest incarnation of ska, dating from the late 1980s/early 1990s to present. This is where the whole ska scene really starts to get fragmented. Many bands are called ska, or call themselves ska, and there aren't really hard and fast rules as to what is or isn't ska these days. Some bands are switching back and forth between ska and punk, sometimes even on the same album. Basically, however, the third wave ska band is now a punk rock band with a horn section or with some other funky instrument. No longer is the horn the primary instrument of the band. That role has been taken over by the guitar. The rhythms are often the same off-beat tempo as the first and second wave, but they're played a lot quicker. A lot of the punk influence in ska can be traced to the Mighty Mighty Bosstones and their unique brand of ska-core. There's also a resurgence of the two-tone image, but these kids aren't the old skool rude boys who'd kick your ass at the drop of a hat. Other splinters have grown into the ska genre as well, such as the straight edge movement, skinheads, skanking, etc.
Notable third wave bands:
sources:
http://www.geocities.com/arrayedroots/ARSSka.html
http://www.2-tone.info/
Oolong
http://www.skullyrecords.com/sowhat.htm