So it starts in the 1920s with New Orleans jazz.
New Orleans jazz was typically with a 2-beat meter, rather contrapuntal and led by the the trumpet and cornet, and later by the clarinet and trombone. The rhythm section was a tuba with the bass line, the drumkit and a banjo, although the backline soon consisted of guitars, piano and a double bass instead.
This fed into the Chicago style, heavily dominated by Louis Armstrong, with soloists having a more prominent role, supported by the band and saxophones coming to the fore. (Brief history of saxophones: http://www.bsmny.org/exploring-music/features/iid/saxophone/2.php) Also instead of being in duple metre, the double bass played with 4 in a bar. As ensembles grew in size, the tuba replaced the double bass due to its bigger volume and arrangements became more common, leading to call and response between sections.
As many people migrated from the South to the North, New York City became a new jazz hub, with the development of Tin Pan Alley where some of the biggest names started out, including Irving Berlin and George Gershwin. Big Bands became more popular, with Paul Whiteman, the ‘King of Jazz’, who had a dream of symphonic jazz, fusing classical and jazz styles together. Hence string sections became more common in big bands, with vocals playing a more prominent role. Also instead of the originally contrapuntal New Orleans jazz, there were soloists accompanied by the big band, with each soloist improvising and developing the melody each time.
Between 1935 and 1946, this was the swing era. Many pieces were covered from the Great American Songbook, which had all the jazz standards, with bands helping to launch the careers of others, such as those of the Dorsey brothers who helped Frank Sinatra begin his career. Other notable big bands included those of Duke Ellington, Count Basie, Cab Calloway, Benny Goodman and Glen Miller, among many others. However as the tempo increased, with more improvisation, more raunchy lyrics and wild dancing, other musicians began to regard swing as merely light entertainment to sell records, including the likes of Stravinsky.
Hence by 1940, with the war ongoing and a 20% rise in amusement tax, money was scarce, so staffing musical events was difficult and more expensive, plus there were the musician strikes of 1942 and 1948. This led to the decline of the swing era, giving way to what we now recognise as pop music and rock n roll, and bebop as a reaction to swing, increasing the tempo so it was no good for dancing, with the music becoming more virtuosic.
The 1950s and 60s saw the rise of the crooners and jazz vocalists, ranging from Frank Sinatra (who also dabbled in pop), Bobby Darin, Dean Martin, Nat King Cole and Ella Fitzgerald. The swing era had also merged with the blues, producing Western swing. Though the 70s saw the revival of the swing era; neo-swing leading to rockabilly and ska and rock. Swing became particularly popular again in Germany, who entered Roger Cicero (known for his 40s and 50s swing style) for the Eurovision contest in 2007.
Here’s a Youtube playlist of the swing standards: