When people talk about the Dons, it tends to be through a bit of a nostalgic haze. Remember those 1980s days when they broke the Old Firm stranglehold as the club Alex Ferguson managed before joining Manchester United? Pittodrie's Scottish title-winners? Aberdeen triumphing in Europe?
It's all a long time ago, but maybe we're on the brink of some sort of sequel.
You have to go back to 1984-85 for the last time Aberdeen won the Scottish league title, but now they're top and four points clear of Celtic -- and although the defending champions have a couple of games in hand, Aberdeen are flying.
Their last eight Scottish Premier League games have brought victories and clean sheets -- that's 630 minutes of league football in which they haven't conceded a goal. Their last winless league game, a 2-1 setback at home to Celtic, came in early November.
That sort of defensive defiance is unmatched anywhere: only French outfit St Etienne and Moldovan club Milsami can come close. St Etienne have strung together a sequence of six clean sheets and Milsami seven.
So what's the secret? "It's probably just a combination of a few things -- getting back to basics and looking at our shape, concentrating more on what we are doing when the opposition has the ball," Aberdeen manager Derek McInnes told CNN.
"The biggest drain on confidence is conceding cheap goals that mean you drop points. The biggest way of gaining confidence is getting a few clean sheets on the spin."
McInnes is quick to stress that although the spotlight inevitably falls on his team's defence and goalkeeper, Aberdeen's is a collective effort, describing their sequence of results as "a reflection of the whole team."
He adds: "It's an unusual run, but you should always strive to improve. Last year, our defensive record was excellent and now we are building on that. And there has been stability [in personnel]. Any time a team has a good defensive record, consistency of selection helps."
Scottish football hasn't had the happiest of times in recent years.
Dwindling attendances and the implosion of powerhouse club Rangers, liquidated at the end of the 2011-12 campaign, added to a growing feeling of crisis.
Rangers, re-formed, were admitted to the fourth tier of the Scottish game at the start of the following season, robbing the top division -- for the time being, at least -- of its Old Firm rivalry.
But the continuing resurgence of Aberdeen has added a vibrant splash of color to this season as expectations that Celtic would stroll to another title have, so far, been confounded.
Their attendances have never dipped below 10,000, hitting a high point of a little over 19,000 for Celtic's visit.
Asked whether his side's challenge has pepped up interest in the Scottish top flight, McInnes says: "In terms of stature, the perception of the league will be better when the Edinburgh clubs [Hibs and Hearts] and Rangers [all three are currently in the second tier] are back.
"But there are a lot of good stories -- Dundee United, Inverness, Hamilton and ourselves are up there challenging. We're glad to be in the fight, and I'm really pleased with what the players have given me."
Familiarity has helped Aberdeen develop their watertight defense, with Mark Reynolds, Andrew Considine, Ashton Taylor and goalkeeper Scott Brown all having played in each game of a run that has taken the team's overall goals against record to just 17 in 21 matches.
But it's not just about that, says central defender Taylor, a summer arrival from English League Two club Tranmere Rovers.
"We are putting our bodies on the line to stop the ball going into the net," he told Aberdeen's Press and Journal. "I tend to focus on what I have to do against each player, while we have got a lot of good players in front of us who can score goals in any game."
"I certainly didn't think I would keep so many clean sheets," keeper Brown told the paper.
"I've always wanted to better myself and push myself as hard as I can, and I thought I could do that with Aberdeen. A big part of the appeal was to have [legendary Aberdeen goalkeeper] Jim Leighton working with me as goalkeeper coach."
It's all a far cry from earlier in the season, when McInnes was getting hot under the collar... because Aberdeen were conceding too many avoidable goals.
Speaking after a 3-0 defeat at Hamilton Academical in October, he said: "We as a team know we can't go through the season losing cheap goals if we want to be successful. Losing soft goals is something that has to be dealt with.
"We need to make better decisions, and we need to show far more determination when we are defending."
Now Aberdeen are targeting the world's best winning league streak, currently held by Uruguay's Nacional with 12 consecutive victories.
But neither McInnes nor his players are talking publicly about their chances of becoming champions of Scotland again after 20 years -- there's a long way to go, we'll take one game at a time, that sort of thing.
Former Rangers, West Bromwich Albion and Dundee United player McInnes guided the club to their first silverware in 19 years when they beat Inverness Caledonian Thistle in the Scottish League Cup final last year.
And with his side flying high, it's no surprise that he's the current Scottish Premiership Manager of the Month.
He believes the fact that the Scottish game gives chances to home-grown managers has offered them an environment in which to flourish, with former Hamilton Accies boss Alex Neil the latest to be headhunted by an English club when he joined Norwich City earlier this month.
"I got an opportunity as a player-manager [at St Johnstone] first of all," he says. "People get chances to build teams, and Alex Neil did fantastically well.
"He was ingrained in that club, and the biggest compliment you can pay him is that his team was like an extension of him -- very competitive, very disciplined. You knew it would be tough against them."
It's not only in the Scottish top flight that things are looking up -- new national manager Gordon Strachan has also brought renewed optimism to the Scotland team.
"We've had a few players involved in Scotland squads, and the challenge for them is to force their way into a team that's doing well," McInnes says. "There is a good spirit there, and I think there's more to come from them."
There could be even more to come from Aberdeen, too.