Grand Alliance: Order
Aligned as one, the civilised races of the Realms go forth to claim the lands and restore Order, Sigmar's Sigmarines Stormcast Eternals leading the fray.
Armies of the Aelves
Look! It's the Elves Aelves! As fancy and effeminate as ever, and now split into 11 12 (!) different factions.
Darkling Covens - Aelven sorceresses that didn't agree with the rules of the Eldritch Council and went to do their own thing. They have enthralled whole armies of aelven followers which they use to push their coven's agendas. They have male sorcerers now.
Daughters of Khaine - The followers of Morathi. As crazy as ever.
Eldritch Council - Groups of sorcerers and their followers that have established enclaves throughout the Free Cities. Still some of the best magic users around.
Lion Rangers - Warrior mystics that roam the land with their lion companions offering aid to those they can. Currently fighting alongside the armies of Order.
Order Draconis - A proud knight order, few fled to Azir during the Age of Chaos because they held their ground and defended their holds like men and survived.
Order Serpentis - The shadow of the Order Draconis, they're merciless but still proud. They had whole dragon units, but because there are few left they (re-)created the War Hydras and Drakespawn with the help of the Darkling Covens to fill the gap. They have a thing going with the Covens and help each other from time to time.
Phoenix Temple - A warrior order that worships the Ur-Phoenix (which is implied to be a God-beast in the Mortal Realms). Their warriors appear to have sworn oaths of silence and are inducted into the order after almost dieing through ice and fire before being revived by a pheonix of the temple.
Scourge Privateers - Apparently now monster hunters. They go around capturing fantastical beasts and selling them (either whole to be tamed and trained or in bits and pieces) to different organisations for some coin.
Shadowblades - AoS' Night Lords. They usually stalk the shadows of the cities of Order watching for who be in cahoots with Chaos or Nagash and gruesomely murder them and put their bodies (or what's left of them) on public display as a warning. But they're good guys.
Swifthawk Agents - The messengers and scouts for the armies of Order. They also maintained waytowers throughout the Realms that still stand today and serve as bastions.
Wanderers - What's left of the Wood Elves. Apparently, the trees don't like them so much anymore.
Idoneth Deepkin - Literally sea elves reborn!
Armies of the Duardin
The Dwarfs Duardin are back, and are as grumpy and beardy as ever.
Dispossessed - Classic, "proper" dorfs. Still holding grudges and generally being grumpy. Some of their heavier units have migrated into the Ironweld Arsenal list.
Fyreslayers - Expanding on the Slayers, here's a whole faction of them (and no, they don't slay fire, incorrectly spelled or otherwise). Ride atop giant salamanders and possess very little in the way of clothing. Possibly beardy heretics, as it looks like their religion's founding might have had a bit of fuckery involved...
Kharadron Overlords - Steampunk dorfs that lead a meritocratic society. They have airships, guns, blimp-jetpacks, and they... okay, they're Squats, guys. They're basically Squats.
Armies of Man
Now relegated to "silly normals" status, mankind are now the Imperial Guard to the Stormcast's Space Marines.
Collegiate Arcane - Assorted wizards and magical scenery. You can now play a full army of dress-wearing spellslingers! Rejoice!
Devoted of Sigmar - A little bit out of place in this new, Noblebright world inhabited by giant immortal armoured warriors who eat Chaos and shit out redemption. The Devoted are the classic raggedy zealots, led by warrior priests. What, those other names engraved on the War Altar next to Sigmar's? I don't know who you're talking about. What's an Ulric? Also one of the model lines updated indirectly by AoS in the form of the Excelsior Warpriest.
Free Peoples - What remains of the Empire list. It turns out that thousands of years later, in a totally different place in time and space, men and women still dress in exactly the same silly feathered hats and pantaloons and there has been no cultural shift or development in that time whatsoever. This is despite the fact that the denizens of the Realms are generally described as being barbarians (which the Stormcast have been drawn from) and all other vestiges of human society have been laid into by Chaos hordes. The models still have Empire heraldry and symbols up the wazoo, meaning that Freeguild General that has "Karl Franz" emblazoned across his griffon's armour? Total coincidence... and while we're at it, what the fuck's a Reikland?
Ironweld Arsenal - Where Steam Tanks and artillery ended up.
Seraphon
The lizards are back, but they are now demon space lizards, apparently. Very blue and very angry at Chaos, they appear from nowhere to mulch the gribblies at every opportunity. Due to some kind of racial memory, the Skaven are absolutely terrified of them. The Bonesplitterz are just pissed off that their monsters disappear before they can eat them.
Stormcast Eternals
Games Workshop's new golden boys. Space Marines weep, for in their heart they know they will never be a Stormcast Eternal. They are lead by the Lord-Celestant, their Spiritual Liege, who takes Ghal-Maraz out for a spin like he's borrowing the keys to his dad's Ford Fiesta. Notably, he hasn't been named as of yet, so rumour abound as to who he might be.
Extremis Chamber - It's the Sigmarines, but to the extreme! Totally radical! No, it's The Stormcast Eternals, but on Dracoths and Stardrakes. They came out after the Order Battletome, so they needed to put them in another book, basically.
Stormcast Eternals - It's the Sigmarines! The new poster boys of the setting, and likely the result of several GW board meetings trying to tap into the "male power fantasy" (and annoyingly, by how well sales have been, everything seems to be going according to plan). They are essentially the Fantasy answer to 40k's Space Marines, being nigh-immortal demigods who are viewed with mixed awe and fear by both allies and enemies. Unlike Space Marines (barring one or two examples), they basically can't die under normal circumstance. Upon death, they are warped back to Sigmar's side, smacked about with a hammer reforged, then sent back. Nagash doesn't like this, and takes whatever bits of their soul he can grab on their way out, making them come back more and more like automatons.
Sylvaneth
The Tree People from the Wood Elves, who they now hate due to momma Alarielle saying that they shouldn't play with those nasty meatbags.
Others
Ironweld Arsenal - A bunch of Human and Duardin engineers came together and compared notes. Cannons and general siege machines. Seems to be intended for use as an ally for artillery support, but does also have things like gyrocopters included too.
Bretonnia (Warscrolls Compendium: Bretonnia[1]) - Not a faction in the fluff, as its models are now discontinued and they've gone the way of the dodo. Still have rules on the GW website, meaning you can use them to have your own flavours of knightly orders and stinking peasantry.
Pantheon
Sigmar - The God King of mankind.
Grungni - Crafts weapons and armour for the Stormcast Eternals as repayment for his debt to Sigmar.
Grimnir - Blown up into Ur-Gold pieces fighting Vulcatrix.
Alarielle
Khaine - At least that's what the Daughters of Khaine believe.
Ur-Phoenix