I am going to go in depth and examine in detail the many parts which make up the brilliant whole that is this book; art, production value and the many different writing skills Hickman has employed to bring about this great run.
Art
So what is it about the run that was so great? First off we can talk about the obvious thing, great artwork. Dale Eaglesham partnered with Hickman to launch the run and he immediately found a style which was at once romantic and, dare I say Kirby-esque, while also being modern and grand in a new age way. But above all it looked right it looked like the Fantastic Four should look.
And from that auspicious beginning the artwork continued to thrive. Alan Davis on covers, Steve Epting, Nick Dragotta, Barry Kitson, Ron Garney, Leinel Francis Yu, Neil Edwards, Ryan Stegman and on and on. Later in the series artists like Juan Bobillo and Greg Tocchini were getting flak in the letters column of FF but I think their styles were well suited for the kid-centric nature of the book.

Production Value
First off how about $2.99 an issue in this day and age? And for the amount of content that was packed in Mr Hickman can be assured that this reader got his moneys worth. From reading the letters columns in the book I know that Hickman was very wary of giving his readers bang for their buck, and unless you're Kurt Busiek then there isn't a lot of complaining to be had. (Here is a great article on Busiek-Gate: http://www.bleedingcool.com/2010/09/16/why-kurt-busiek-is-wrong-about-jonathan-hickmans-fantastic-four/ )
Issue 600 was one of the best single comic books I have ever read. At $7.99 it was pricey, but for that price the reader got 100 pages of original content, not a reprint of an issue in back and padding with character profiles, original content! With art by Steve Epting, Leinel Francis Yu and Farel Dalrymple, among others.
Issue 605.1 was another example of a scheme where Marvel likes to extort money from it's readers by creating so-called "jumping on points" which move the plot nowhere and are generally a waste of time. In 605.1 Hickman uses the issue to explore one of the universal Reeds who comes from a parallel universe where Axis powers won World War II. This depiction of Marvel's first family as Nazi sympathisers is truly horrifying and not only is it a tale well told, the reader also gets a look at another side of Reed, albeit through the lens of an alternate history. Without a doubt the best point one issue yet.
Then there is the costume re-design, beautiful integration of the hexagon theme on all of the uniforms, sleek black and white, very Apple. The small touches like Alex Powers special outfit. Brilliant. I've seen a lot of re-designs of the fours outfits and none of them have even come close to the sleek beauty of these outfits.
Writing

Hickman understood that the foundation of the book was the family. "A perfect family in an imperfect world" as he said in his farewell letter to fans. And from that foundation of family the book should grow exponentially into the far reaches of space and time as any good Fantastic Four book should.
It's funny, heartfelt and grand storytelling in all the right measures.
Now what I'm going to do is go through the series in some detail, highlighting specific issues and moments which are of particular note. Spoilers ahead, if you haven't read the series yet, go do that, right now.
When Hickman was given the gig of making the Fantastic Four relevant again it was a longshot. After the failure of the proven team of Mark Millar and Bryan Hitch to illicit excitement from a jaded public Marvel did what I don't think anyone expected, they gave the book to a relative unknown and said "swing for the fences".
Hickman confessed that he had no love for the book prior to writing it and from this point he went back and read the entire back catalogue of books. From that exercise came the chart below.
Hickman got what many see as a 'pilot season' with a five-issue mini called Dark Reign: Fantastic Four in which Reed builds a machine to find out if there was anyway to prevent what had happened with regards to the current Osborn in power status-quo. The results are remarkable as is what happens to the rest of the family while he is in the machine.
In a taste of things to come, Sue, Johnny and Ben are transported into variable space-time where they are changed into pirates and medieval nobles and soldiers in World War II as they bounce around in what is a classic Fantastic Four adventure.
While all this was happening the Richards kids, Franklin and Valeria, are trying to stop Norman Osborn from taking over the Baxter Building which allowed readers to see just how well Hickman understood not just the adults but the kids as well.
From this mini Hickman took the reins of the flagship title along with Dale Eaglesham on issue #570 and began extrapolating on the meeting between Reed and his alternate universe selves. And from here he builds some big ideas;
- The council of Reeds farm entire worlds to feed universes, they fix dying suns and incur the wrath of the Mad Celestials.
- The Reeds perish by the dozens at the hands of the Mad Celestials, infinity gauntlets are harnessed to try and stop the interlopers.
- Reed realises that to truly "solve everything" he must give up his family, an aberration, Reed chooses his family over the greater good, the first to have done so.
- Issues 575-578 "Prime Elements", four one-shots that set up the "War of Four Cities"which will have ramifications for the Inhumans, Namor, Mole Man, The High Evolutionary and The Negative Zone.
- Issue 581 sees Immortus instigate the "Great Hunt" as Reed's father returns revealing that all of the Nathaniel Richards' of all other realities are hunting each other to the death.
- Adult versions of Franklin and Val begin foreshadowing things to come, time travel ramps up.
- Issues 583-587 'Three' the death of Johnny Storm at the hands of Annihilus as Hickman closes off his first main arc.
- Issue 588, in my opinion one of the strongest, most emotionally charged and well-executed silent issues ever. Great symbolism with Spider-Man and Franklin having both lost uncles.
- FF is launched and the council of Reeds begin the "War of Four Cities" in their quest to build the super-weapon "Sol's Anvil" which they hope to use to stop the Mad Celestials from claiming their lives.
- A symposium of super-villains consisting of Diablo, Mad Thinker, The Wizard, Dr Doom and the High Evolutionary is arranged by Reed and Val to help stop the remaining Reeds.
- The Kree Supreme Intelligence is reborn using the minds of two of the remaining three Reeds. The Kree set course for Earth, their goal to extinguish all life on the planet.
- Black Bolt returns from the grave and takes Attilan to Earth to face his destiny.
- Fantastic Four 600 sees the return of Johnny Storm now leading the Annihilation Wave from the Negative Zone with a leashed Annihilus at his feet.
- Annihilation Wave and Universal Inhumans meets Kree Armada.
- Galactus is summoned by Reed to help fight off the Armada.
- All the while Val, Nathaniel, Doom and the Future Foundation have been playing stalling tactics with the remaining Mad Celestials. Doom sacrifices himself to buy the time required.
- All the players are on the board, Galactus fights the Celestials, he loses to the newly formed Super Celestial. Sol's Anvil is fired and breaks apart the Super Celestial. All seems lost as the heroes of Earth fall until only Sue remains standing. Then even she falls. Enter future Franklin.
- Franklin summons his Herald, Galactus and tears the remaining Celestials apart!

There is symbolism by the bucketloads, symmetry and numbering play a big role in structure and Hickman also uses the book as a lens to look at the world we live in. Of particular note is a speech by the Mole Man in issue #575 about the state of our communities and social priorities;
"So I ask you-- which is better? Simple creatures who know nothing more than community and the comfort of their family or enlightened individuals who abandon those things for their own personal gains?"And then there is Hickman's re-imagining of the Yancy Street Gang as failed hedge fund managers and dot-commers hit by the recession, delicious witty stuff.
Hickman nails each and every character he gets his hands on. From the core family and the Future Foundation to Spider-Man and Namor, Hickman hits pitch perfect dialogue. One of the great examples that comes to mind is when Sue knocks Namor on his arse and tells him that she is in charge and Namor's response is; "God you are magnificent." Sue responds with an eye-roll.
And on top of that Hickman never loses the heart, all of these actions that lead to cosmic adventures and showdowns come from genuine character motivation that isn't forced, the logic behind it all is sound and I think that Hickman is one of the best logically minded writers in comics, on top of which he's got a hell of an imagination.
Like I said before, if you somehow find yourself at the end of this article and you still haven't read this run, do yourself a huge favour and go check it out.