Typically when this question comes up on this or other forums someone will post that it will not work because the .38 Super is a tapered case (wrong) or because it has no rim (wrong).

Two brands of modern factory .38 Super ammo will chamber in most modern (1985 forward) S&W .38 Special and .357 Magnum revolvers: Winchester and Magtech. Within Winchester, both the 125 grain Silvertip and the 130 grain FMJ will chamber. The same is true of some Colt's, like the Python. Other ammo brands I have tried, such as Remington, UMC, Federal, Armscor, Corbon, Fiocchi, PMC, and Aguila will usually not chamber.

I have fired .38 Super out of .357 Magnum revolvers, and it works fine, accuracy is not degraded, extraction is no problem. I'm not recommending it for everybody else, but it as stated above it has worked fine for me. Note the headstamps pictured below...