Ostensibly, they have been to win every trophy available, but results have clearly not borne that out. The Gunners have been to three cup finals since their last victory (one Champions League and two League Cups), but the trophy cabinet at the Emirates is barren.
Progressively, systematically, tragically, the great Arsenal sides of the early 2000s were dismantled.
Vieira, of course, was the first to go. Over the next couple years, the Arsenal faithful would wave goodbye to several all-time greats, including Freddie Ljungberg, Robert Pires, Ashley Cole, Lauren and the greatest of them all, Thierry Henry.
None of these players retired—all were sold. While great footballing careers inevitably come to an end at some point (Dennis Bergkamp called it quits in the middle of this selling period), players' careers at Arsenal ended prematurely.
That was only phase one of Arsene Wenger's grand rebuilding plan, which coincided with the club's massive investment (i.e. the assumption of long-term debt) in the Emirates Stadium.
The product that Arsenal put out in the ensuing years was entertaining and worthy of praise, but its quality had clearly dipped. During the 2006-07 season, the Gunners barely scraped their way to a fourth place finish in the Premier League.
For the first time during Wenger's tenure as Arsenal manager, he had not finished first or second.
The signs of progress were still apparent, however.
Players such as Samir Nasri, Robin van Persie, Emmanuel Adebayor and Mathieu Flamini blossomed into fine players, capable of competing against any side in England when on the pitch together.
And little Cesc Fabregas was always the jewel in the crown. The Catalan maestro was clearly the best player on a team that included several internationals. He embodied the Arsenal way—the new style with which Wenger hoped to win the Premier League.
But that dream splintered over time, as the new generation became discontented, and the sturdy, stately man at the helm lost his taming powers.
This time, however, something different and alarming was happening: Rather than leaving around the age of 30, players were jumping ship before or during their prime years.
Ashley Cole was perhaps the first to do so, but that was before Arsenal's decline began in earnest.
Flamini left on a free transfer, breaking up one of the most promising midfield partnerships in England. Then followed Adebayor under extremely contentious circumstances.
Kolo Toure, a rock in defense for years, finally had enough of William Gallas. Spectacularly, Nasri and that most prized and beloved captain, Cesc Fabregas, waved goodbye in the summer of 2011.
A poisonous trend was forming: Arsenal were selling their best players after every season. But perhaps that would stop with the ever-loyal Robin van Persie, the last great player to win a trophy in an Arsenal jersey.
I don't have the inclination to go anywhere. This is the best team for me to be in. The bottom line is that I want to win trophies with Arsenal, not with anybody else. I know you can win trophies in many countries and in many ways, but I want to do that in our way and in an Arsenal shirt...
Anything we win here will come from the heart and that's what I want. It's my dream and I see no point in speaking about other teams when I have these dreams.
Yet, £24 million for Arsenal and £200,000 per week for van Persie was apparently enough to destroy that veneer. Alex Song quickly followed him out the door.
Every year, the product that the team produces gets worse, and it isn't hard to see why. Sell your best players, your captains, your leaders, your talismans, your brightest young talents and quality will suffer.
Perhaps, the nadir of the Gunners' steady and tragic decline came this week against Bradford City.
Some Arsenal fans might have thought that the home defeat to Swansea, capping the team's worst ever start under Arsene Wenger, was the worst things could get.
But there is absolutely no defense for Arsenal's strongest lineup succumbing to opposition in the lowest professional division of English football.
So what does Wenger want for Arsenal?
One can be sure that he wants to win: Every groundskeeper that has stooped to pick up a maimed water bottle knows that.
But John Brewin of ESPN FC put Wenger's mentality succinctly in his column after the Bradford embarrassment:
That [ex-Arsenal players] no longer play for Arsenal is the story of a club where footballing ambitions have diminished while financial commitments are being met.
This, in essence, is why a club that finished first or second in the Premier League from 1997 to 2005 has not done so since.
This is why Wenger recently lamented the dismantling of his teams, which had so much unfulfilled potential, "after five or six years' work."
This is why the team, brass and fans have slowly (and tragically) come to treat fourth place as the most important "trophy" that can be attained.
This is why Arsenal lost to Bradford City on Tuesday.
Arsenal's chief executive, Ivan Gazidis, spoke to fans on Wednesday in a meeting arranged before the Gunners' disastrous trip to Bradford (via ESPN FC):
Tuesday night was not good enough and it made us all upset and angry. I would like to apologise to all of you, especially the fans who travelled up there.
His words are probably appreciated, but they have meant nothing and will mean nothing until he, the board and owner Stan Kroenke (wherever he is) finally act to right the wrongs endemic within their organization.
Until the club makes some truly reverberating changes from the top down, meeting financial commitments and backing into fourth place will constitute success for Wenger and Arsenal.
Do you really want that?