In the mid-19th Century a fellow named Rollin White came up with an idea- bore a revolver cylinder all the way through so you could load metallic cartridges from the rear. S&W saw the virtue in this and procured rights to the patent- giving them exclusive use of the concept (in America, at least) until 1869.
Colt, then the largest manufacturer of revolvers, had originally scoffed at the idea. Their front-loading cap-and-ball revolvers were doing well, after all. Why would people switch from their tried-and-true to this new-fangled technology?
This turned out to be a big mistake, and Colt and other revolver companies made several attempts, none successful, to circumvent this patent. As you can imagine by the time the patent expired Colt was eager to enter the market with their own cartridge revolvers. Yet by some monumental screw-up they did not have a gun ready and waiting when the patent expired. They also had huge stocks of parts for their cap-and-ball revolvers. So they did the obvious thing- they manufactured cap-and-ball guns suitably modified to fire metallic cartridges.
To do this they cut away the back of the cylinder where the nipples for percussion caps were normally placed, bored them straight through at a uniform diameter and built a breech-plate with a loading gate to place behind the cylinder. Voila! Instant cartridge revolver.
These were originally made with 1851 Navy frames and barrels and chambered in .38CFC, a short cartridge with a heeled bullet. There were a number of variations, and eventually conversions of Army revolvers as well as a purpose-built open top revolver based on the old-style frame.
These guns remained popular long after the introduction of Colt’s Single-Action Army revolver, which was mechanically quite similar to their early guns but enclosed the cylinder in a solid-frame.  Part of the reason for this was price- a Richards-Mason Colt could be purchased for about $5 whereas the new SAA cost $25. For a modest fee Colt would also convert a customer’s cap-and-ball gun for cartridges. Remington also jumped on the bandwagon and offered their own, arguably superior, cartridge conversion revolvers.
These guns largely vanished into obscurity, known mostly to fans of spaghetti westerns and arms historians. Then awhile back some gunsmiths started offering conversions for cap-and-ball reproductions. Two companies currently offer conversion kits for Pietta and Uberti cap-and-ball revolvers.
Howell (http://www.howelloldwestconversions.com/shop/products.cfm?catid=261) offers two types of conversions. The first type consists of a cylinder and base-plate with individual firing-pins for each chamber. To load these the cylinder must be removed from the gun, the baseplate removed from the cylinder and the chambers loaded, then the base-plate is replaced and the cylinder reinstalled in the gun. The process is cumbersome, but does allow one to switch back-and-forth between cap-and-ball or cartridges and requires no modification of the firearm.
Howell’s second type of conversion permanently converts the revolver to fire cartridges, and is very similar to the original Colt or Remington conversions. These do require some metal-working capability, and Howell offers fixtures to help with this. Essentially it involves boring and tapping some holes in the breech-face and relieving the blast-shield behind the loading gate to allow cartridges to be inserted.
Kirst (http://www.kirstkonverter.com) also offers a cartridge conversion kit that is almost a drop-in conversion. It still requires that the blast-shield be relieved behind the loading gate, but this is easily done with fairly basic tools.
Both of these companies offer proven products that function well, but there are limitations. First is that the cylinders are too short for some modern ammunition; care must be taken to select or reload your own ammunition that is short enough to fit in the cylinder. Also Navy caliber revolvers (.36) fire bullets slightly larger in diameter than a modern .38 Special uses. Generally these conversions are chambered for .38 Colt, which is pretty expensive ammunition if you don’t reload your own. You may be able to shoot commercially loaded .38 Special Hollow-base wadcutters in them; the overall length is short enough and the hollow-base of the bullet will expand to fill the bore properly.
Another limitation is a function of the construction of cap-and-ball reproductions. Revolvers have what is known as a ‘forcing cone’ at the base of the barrel to guide the projectile from the cylinder into the rifled bore of the barrel. In modern revolvers the forcing cone is tempered steel, and thus can use any modern jacketed ammunition that the gun is rated for. But on cap-and-ball revolvers the forcing cone is not tempered, and firing high-pressure ammunition or jacketed bullets can split the forcing cone, ruining the barrel and rendering the gun unsafe to fire. Guns outfitted with these conversion should use lead bullets only, in low-pressure loadings that do not exceed 1000 fps at the muzzle.
Lastly these conversions are for steel-framed guns only- mounting one in a brass-framed gun is dangerous and should not be done.
Legally in most jurisdictions in the US cap-and-ball revolvers are not considered firearms. Once you convert it to fire cartridges this may change, and my change the rules under which the gun may be sold or transferred. The simple remedy for this is to dismount the conversion and fit the original cylinder to the gun and include the conversion parts in the sale. In some states it is illegal to do this conversion; check  your local laws before investing in a cartridge conversion!
The use of obsolete cartridges, lead bullets only etc. can limit the appeal of these guns, especially for folks that don’t reload their own ammunition. But have no fear- Cimarron Firearms (http://cimarron-firearms.com) offers factory-made cartridge-conversion guns in calibers like .38 Special and .45 Colt, as well as a variety of ‘western’ calibers. These guns do vary a bit dimensionally from the originals; the cylinders need to be long enough for the modern loadings, and they are a bit more robust to accommodate the pressures of current ammunition. You can use jacketed ammunition in these guns without fear, though use of +P ammunition will dramatically accelerate wear on these, particularly the open-top style guns. They should be fired with standard-pressure loads only.
Years ago my wife bought me one of these, a Cimmaron .38 Special Richards-Mason 1851 Navy conversion with a 7-1/2 inch barrel. It’s a well-made gun, and after I made a cross-draw holster it was my constant companion when hunting. Despite it’s rudimentary sights it was accurate and a real pleasure to shoot. Â For some time it was my ambition to purchase another and convert it to a ‘belly-gun’ by shortening the barrel and converting the handle to a ‘bird’s head’ profile. Eventually I did the conversion on the original gun (see picture at top) and it has become my favorite revolver. Still a pleasure to shoot and as accurate as before (I improved the sights) but much handier. My wife Linda always found the gun too heavy with it’s long barrel, now loves to shoot it as well.
It is a bit more of a problem to reload since it no longer has an ejector, but until it gets quite dirty spent shells fall free with a tap on the cylinder, and I’ve never had one get so stuck that I could not flick it out with a fingernail.
One last thing- these guns are not modern firearms! It may not be safe to carry them fully loaded with six rounds. Leave an empty chamber under the hammer, just as you would with a Single-Action Army or other period/reproduction revolver.
If you are a Cowboy Action Shooting competitor, a history buff or just want a ‘cowboy gun’ that is a little different these guns are a cool option to a Single-Action Army or their numerous clones and near-clones.