That Zelda games aren't always developed by Nintendo alone, isn't a new concept. Ignoring the abominations made by Animation Magic and Viridis, the first successful cooperation between Nintendo and some other company to make a Zelda game was in 2001 with Oracle of Ages & Seasons on the GameBoy Color, which was developed by Flagship - a studio formed by both Capcom and Nintendo. This studio later would develop Four Swords and The Minish Cap for the GameBoy Advance, before it got dissolved.
In the following years we also had the studio Vanpool, which developed the Tingle spin-off series for the Nintendo DS and DSiWare, where Tingle's Rosy Rupeeland is probably the most noteworthy title. Then GREZZO took over the handheld Zelda realm and co-developed the Four Swords Anniversary Edition for DSiWare, as well as Ocarina of Time 3D, Majora's Mask 3D and Tri Force Heroes for the Nintendo 3DS.
So, on the handheld systems outsourcing the development has been going on for the majority of Zelda titles. But things have gotten more remarkable in the last year, where a total of five different game development companies aside from Nintendo have been spotted working on the The Legend of Zelda franchise:
- Koei Tecmo developing the Hyrule Warriors series
- GREZZO co-developing the Nintendo 3DS Zelda games
- Monolith Soft co-developing Breath of the Wild
- Tantalus Media co-developing Twilight Princess HD
- Jupiter developing Zelda Picross
Koei Tecmo with its development teams "Omega Force" and "Team Ninja" is currently working on the DLC for Hyrule Warriors: Legends and afterwards will most likely start developing Hyrule Warriors 2 for NX. This spin-off series certainly is going strong and will probably deliver the best fan service to Zelda fans for years to come, where all the many fan favorites get to be playable on Hyrule's battlefields.
GREZZO has finished the development of Tri Force Heroes last year and is now working on their own game, Ever Oasis. But we might see them return to the Zelda franchise at some point in the future, if they aren't already developing something on the sidelines.
Monolith Soft known for their extensive worlds in Xenoblade Chronicles is currently supporting the development of Breath of the Wild, where Hyrule never has been larger and certainly will profit from the additional workforce. Before they also assisted in the development of Skyward Sword and A Link Between Worlds, but were only credited under "Special Thanks". Their involvement seems to be somewhat more important this time around.
Tantalus Media delivered the HD remaster Twilight Princess HD, where it's possible that they are also supporting the development of Breath of the Wild with high resolution texture work. Future HD remasters like a potential Skyward Sword HD might also get outsourced to this Australian studio.
Finally, there's the Jupiter Corporation known for their many Picross titles, which now just tacked into the Zelda franchise with My Nintendo Picross - The Legend of Zelda: Twilight Princess. It's entirely possible that they are currently developing a new Picross game based on another installment of the Zelda series, e.g. The Wind Waker. Potentially all Zelda games with 3D visuals could end up getting their own Picross game, so that Zelda fans will have something to spend Platinum Points on in the future.
And that's just what we know so far. It has been hinted by Nintendo that a Zelda anime movie could be a possibility, where some Japanese animation studio might be working on something as well. And hopefully one day we can see "Retro Studios" on the list above.