The timeline of the Zelda franchise has been a topic of debate ever since Ocarina of Time (and maybe even earlier), but came to an end in 2011 with the release of Hyrule Historia and the official timeline that put it all into picture. And this certainly this had removed some steam from the Zelda discussion boards all over the internet.
But with Breath of the Wild Nintendo has reignited the flame of timeline theories, where for almost a year now the fans debate over where Breath of the Wild falls into the timeline, ever since the game got showcased at E3 2016. Even after the game has been released, the only thing that became clear was the fact that it takes place over ten thousand years after the rest of the series in an age of ancient technology.
It has resolved some mysteries from last year's E3 - for example it should be clear now that Hyrule Castle and Hyrule Castle Town probably aren't really the one from Twilight Princess, though they certainly share a lot of similarities in design.
But the clues still remain all over the place. The existence of the Koroks points at the Adult Timeline, while the resting place of the Master Sword is very similar to the one from the Fallen Hero Timeline. In the English translation Zelda mentions that the Master Sword has been "steeped in the glowing embers of twilight", though other translations just mention "shadows" at this part. And the Divine Beast Vah Medoh is probably named after Medli (spelled Me-do-ri in Japanese and even called Medolie in French and German), while places on the map are named after many different persons and locations from almost all Zelda games, including handheld games like Link's Awakening, Oracle of Ages, Oracle of Seasons, The Minish Cap, Phantom Hourglass and even Tri Force Heroes.
If you take amiibo goodies into consideration, things get even crazier, because not only can you summon Wolf Link from a different era, you can obtain equipment of many different heroes from the past over all the timelines. But of course some gimmick like this probably shouldn't be considered as true canon material.
However, the problem remains the same. You can't really pin down the timeline placement of Breath of the Wild in any of the three established branches. And the discussions are going on, which is probably even intended by Nintendo.
But the real question is... Does it even matter?
From the perspective of the game, everything that happened in past Zelda games has happened such a long time ago that it doesn't feel like the timeline split should matter even more. Breath of the Wild has literally put thousands of years between itself and the rest of the series. Do we really need to keep up three different timeline branches for this? From this new perspective it's like all the past Zelda games became mere legends, where all of it may have happened, completely independent from the timeline split.
Last year after the E3 I came up with timeline merge theory, where the new game(s) take place in a unified timeline and where everything from the past Zelda games is coming together. This was supposed to explain all what we've seen at the E3 and I even came up with various story concepts for how such a thing could happen.
And while Nintendo didn't go this route with its story, it seems like they still took a similar approach. They created a Zelda game, where the rest of the series takes places at such a distant past that the timeline split doesn't really matter anymore. Breath of the Wild essentially takes place in a new timeline, a reboot so to say, where the entire past of the Zelda series has become the "lore" of this new universe.
It still would be nice to learn more about what happened 10,000 years ago and even before that. How did Calamity Ganon came to be? What happened, before the Sheikah technology was created? Maybe the DLC or a future Zelda title will explore this and maybe at some point Nintendo will really introduce a timeline merge to the story. But until then the most convenient and simplest explanation is that all the previous stories are just lore and legends to this new world.