World War II, really.
There have been a very few guns chambered for it since then, mostly commemorative guns (Winchesters "The Duke" Model 1894 lever action), and some special order single shot rifles are about the only ones I know of.
The 32-40 began life in the 1880s as a black powder Ballard target rifle cartridge. Winchester also adopted it, and in 1894 it was one of the original two rounds chambered in the 1894 rifle (the other being .38-55, the .25-35 and .30-30 didnt' come along until 1895).
Marlin, Savage, Ballard, Evans, Remington, and possibly others chambered a variety of rifles for this round, mostly either lever actions or single shots.
It was one of those cartridges that made the transition into smokeless powder, but never really regained the popularity it once had.
After WW II it became functionally obsolete. You can still find ammo for it, cases are made, etc., but I don't think any of the big ammo companies actually makes ammo in this caliber any more.
One of the rifles on my long-term wish list is a Savage 1899 in .32-40.
