This.
Unless you've been living under a rock since 2008, this is the Pip-Boy 3000, a wrist-mounted personal computer that displays your stats, inventory, and map, all while the lovable Vault Boy provides handy visualizations.
And it is all completely wrong.
The Pip-Boy from Fallout 1 and 2 was NEVER a wrist-mounted device. It was a handheld box, which is obvious if you have ever seen the classic Pip-Boy. It is far too wide and cumbersome to be carried on the wrist.
Why did Bethesda change this? For the same reason that it seems they make all their decisions by: It looked cool. The same reason that a gang living in a vault whose doors have never been opened since the bombs first fell somehow has access to leather jackets and custom snake patches. The same reason that the denizens of Rivet City never cleaned up all the junk in the lower levels even though clearing this junk out would provide ample space for growing crops. Hell, the same reason that all of the settlements in Fallout 3 seem to have no crops anywhere near them and yet are somehow able to eat.
But I digress. To give credit to Bethesda, they did attempt to fix this by establishing that the Pip-Boys in Fallout 3 was a later model (3000 instead of 2000), and while this still didn't wash out the sour taste it had left, it would make sense that the higher-numbered (and therefore later built) vaults on the east coast would get the newer models while the earlier ones (such as Vault 13, where the Vault Dweller emerged from in the first game) would get the more primitive models. It allowed allowed this new version to exist without bending already established lore in half...
...until New Vegas and 4 happened.
Fallout: New Vegas takes place back on the West Coast, and after completing the mercifully short player creation sequence in Doc Mitchell's house, he naturally hands you a Pip-Boy... 3000. He even states that it was the one he was given back when he was growing up in Vault 21. It would be possible to write this off by saying that the new models were introduced fairly early on and that some vaults on the west were also given the 3000 models, but not only is this never established in any of the games proper, but the denizens in Vault 11 are all shown to be wearing the 3000 models instead of the 2000 models.
The use of the Pip-Boy 3000 in New Vegas was not Obsidian's fault; they were only allotted 18 months to make the game, and making a 3D version of the original handheld Pip-Boy would have taken up precious development time they could be put to better use making the rest of the game as good as it could possibly be. I don't blame them for this, nor does it take away from the magnificence that the rest of New Vegas was. But it does show a total lack of foresight or basic understanding of the universe that they inherited on Bethesda's part to allow something like this to happen. All it would take was a single line in Fallout 3 or 4 to clean this whole mess up, to establish why some vaults have earlier handheld models and some have later wrist-mounted models, and why this doesn't sync up with their numbering or order of construction.
But not only did they not do that, they managed to dig the hole they were in even deeper.
Ladies and gentlemen, allow me to introduce you to the very first model of the Pip-Boy, courtesy of the Fallout 4 introductory cutscene:
This should raise some questions: why is it that the Pip-Boy 1.0 was wrist-mounted, and yet the Pip-Boy 2000, a later model, was handheld? Why was the jump back to wrist-mounted made again after the 2000 model? Is the numbering misleading? Is the 2000 model is simply a budget handheld model while the higher-grade main line was wrist-based, and the 3000 numbering applied to all the 'standard' ones, and there were merely different revisions in this line? This would seem the most likely and logical, especially since the model in Fallout 4 is specifically referred to as the 'Mark IV' model. However, as per usual, Bethesda spent no time whatsoever explaining anything, and simply threw a bunch of ideas at the wall and left other people to sort them out.
The Pip-Boy in Fallout 3 onward is a perfect microcosm of Bethesda's attitude towards Fallout's lore: make it 'cool' at the cost of world consistency. Who cares about established lore when you can make it LOOK good? Who cares about making sure your stories all sync up in logical ways, so long as your world looks 'cool'?
New Vegas was proof that the Fallout formula could appeal to a new generation while still remaining true to its roots. But as long as Bethesda remains committed to making their entries superficially appealing at the cost of consistency, such as with the Pip-Boy, it will remain the exception, not the norm.