This one was written by W.C. Handy, who was very important in commercializing blues music and introducing the blues to all of America by incorporating blues elements into popular music. The song refers to Beale Street in Memphis, Tennessee. There are many versions of this song, but I associate it with Jack Teagarden, who recorded many versions of it, and who was one of the most important and pioneering trombone players of the swing era. (wikipedia.de claims that it was his signature song, but American sources tend to say that was "Stars Fell on Alabama.")
Here is a version with Jack Teagarden on vocal and trombone, his brother Charlie on trumpet, and Benny Goodman on clarinet:
Here is another with Jack Teagarden, Joe Venuti, Eddie Lang, and Benny Goodman:
One of the interesting things about Teagarden's different versions is how he sometimes invents new lyrics that were not part of Handy's original song. Here is a lead sheet for the song, from the Firehouse Jazz Band Fakebook. You can see here an eight bar part coupled to a twelve bar blues form (although not a basic one- this has some interesting variations). This was a device Handy used frequently. The shift of key signature between the two parts was also characteristic of Handy's compositions.