Because of the rapid fire capability of the double-action mechanism, it became the mechanism of choice for new revolvers. Today, most modern revolvers are still double-action. Even Colt, the proponents of single-action pistols, switched to double-action models by the end of the 1800s with their Colt New Service Revolver. Models by Smith & Wesson, Remington, Webley etc. were very popular as well.
By the 1850s or so, metallic cartridges began to replace percussion cap technology. Some revolvers, such as the French-made Lefaucheux, were built to use pinfire cartridges. In 1857, Smith & Wesson introduced their first revolver which used a .22 short rimfire cartridge, also developed by Smith & Wesson. This model was a huge success in the market-place and was responsible for establishing the fame of Smith & Wesson. By the mid 1860s, centerfire cartridges became popular and revolvers began to use them as well (such as the Colt Peacemaker). Most of the early metallic cartridges still used black powder as their propellant, but more powerful smokeless powders started to become popular after 1886 or so and revolver manufacturers began to certify their weapons as safe to be used by smokeless powders as well. This meant using new metallurgical techniques of manufacturing weapons to withstand the higher pressures generated by smokeless powders.
As more powerful cartridges were developed, revolvers were built to fire them as well. In the 1950s, the .44 magnum cartridge, introduced by Elmer Keith and built by Remington, was used by the Sturm-Ruger Blackhawk and the Smith & Wesson Model 29 revolvers. Unusually, the Sturm-Ruger Blackhawk was a single-action revolver, rather than a double-action model. Ruger discovered that after Colt had pulled out its popular Colt Peacemaker (another single-action model) out of the market, there was still some demand for single-action weapons and went on to fill that demand. Company legend at Sturm-Ruger has it that Smith & Wesson were experimenting with the new .44 magnum cartridge in secret, but a Sturm-Ruger employee found the empty cartridge cases in a garbage pile and took one to Bill Ruger and the Blackhawk revolver beat Smith & Wesson's model 29 revolver to the market by several months. The S&W Model 29 didn't sell well initially, but in 1971, the movie "Dirty Harry" came out, with Clint Eastwood's character, "Dirty" Harry Callahan, describing the S&W Model 29 as the "most powerful handgun in the world". While this was not strictly true at this point (the .454 magnum was already developed), this line of movie dialog made the demand for the Model 29 to skyrocket, to the point that dealers were having trouble keeping the Model 29 in stock, even after selling them at triple-price! These days, there are revolvers built to fire even more powerful cartridges, such as the .454 and the .5oo magnum, but the Model 29 sales still remain high, 35 years after the movie came out.
Revolvers used to be the weapon of choice in military and police departments around the world, until modern semi-automatic pistols such as the Colt M1911 became more popular due to shorter reload time and higher capacity of cartridges. Police departments in the United States continued to use revolvers well into the early 1990s, when they began to be replaced by semi-automatic pistols. They are still popular in the civilian market as sporting or hunting weapons. In fact, many trainers recommend new shooters to start off with a revolver.