The concept of duo jungling has been around for a while, and while it's been discussed and certainly done, it hasn't been refined and it isn't a popular strategy. If you cannot figure out what duo jungling is from the name, it is when a team has two junglers and three solo lanes, rather than the standard setup, which is two solo lanes, a duo lane, and only one jungler. While some believe that duo jungling is a horrible idea, with the right strategy it is a very viable setup. I myself have never lost a game in which I was part of a duo jungle strategy. If you're interested in trying this out, the following guide will detail exactly how to do so.

Team composition in a duo jungle strategy is very important. Top and mid lane champions can stay the same as in a normal team composition, as these lanes aren't really affected by the choice to have two junglers. However, the champion picked for the bot lane role needs to be one that is comfortable in a 2v1 situation, and consequently it must be one that is able to safely farm and poke from a distance. Champions that fit this role well include Gragas, Jayce, Shen, Kayle, and possibly Yorick. These champions all have melee based basic attacks (marksmen are generally too squishy to be effective in a 2v1 lane), which makes staying safe hard, but all of them have ranged abilities such as Kayle's righteous fury and Shen's vorpal blade that can be used to farm or last hit.
As far as the two junglers go, it is best to choose one who scales off of attack damage and one who scales off of ability power for the sake of diversity. It is also optimal for one to build tanky and one to focus on damage. For example, one jungler could be Evelyn, who generally builds tanky and scales off of AP. The other could be Tryndamere, who can be built to do high damage and scales off of AD.
It is, of course, recommended that junglers synergize with the rest of their team composition as well as each other.

At the beginning of the game, one jungler (most likely the AP jungler) will go to the blue buff, getting a leash from whichever lane is closer, top or bottom. The other (most likely the AD jungler) will go to the red buff, also getting a leash from whichever of the outer two lanes is closest. It is optional for the mid laner which buff they want to leash, although it is recommended that they go to whichever buff is more likely to be invaded.
The route for the jungler getting the blue buff is as follows: Blue buff, wight, wolves. The jungler getting the red buff should go from red buff to wraiths and then golems. At this point both junglers will be very close to level three, meaning that they go back to the wraith camp, waiting for them to spawn and sharing all of the experience. Now that both junglers are level 3, the next step is obvious: gank. It is recommended that both junglers gank bottom lane, where the 2v1 is happening, trying to give any kills picked up to the laner so that they can better handle their 2v1 situation. Recalling after this gank is strongly recommended. What happens next is completely up to the junglers; they can either gank one of their 1v1 lanes together and almost assuredly pick up a kill as it would be a 3v1, or they could split up and gank both top and mid lanes. Both junglers here should be experienced, having an understanding of map presence and pressure.

After the beginning of the game is over, almost everything is up to the junglers. Three man pushing in a lane for a tower after a successful gank is a good idea, and if someone manages to kill the enemy jungler and/or one or both of the enemy bottom laners, then getting dragon is a very good idea. The junglers should continue ganking and applying pressure until their buffs are back up, possibly clearing some of the smaller camps on the way in between lanes and backing when needed. If someone manages to kill the enemy jungler during the laning phases, do not hesitate to immediately steal a buff (be sure to leave a singular, small monster so that the buff cannot respawn until the enemy jungler finds and kills it, having to wait another five minutes for the buff to be available again; this is called counteesr jungling). If your junglers are confident enough, they can invade the enemy jungle together knowing that they could probably kill the enemy jungler in a 2v1. After the laning phase is over, buffs can be given to those who need them most. Teams should stay together at all times after the laning phase is over, and if your team makes it into the team fighting phase ahead, then the duo jungling strategy is considered a success! Stealing dragon or baron should be easy with two smites, allowing for great control of objectives. Proceed to destroy the other team.

Pros:

2v1 laner will have a level advantage
More map presence / pressure
Ganks in 1v1 lanes are better, making it a 3v1 instead
Invading is less dangerous
Better objective control

Cons:

Bot lane is a 2v1
Experience is harder to come by early game, being split between both junglers

Personally, I believe that duo jungle is a viable strategy, throwing opponents off guard and making it much easier to get solo laners fed. Perhaps if enough people read this guide and try it out, it will become a part of league of legends, being a viable option for everyone. It is also a great way to change things up if you're tired of the standard lane setup. To those of you who may want to try this, good luck and have fun! :)