The Foundation and the Name:
In Germany, fans are very serious about football being a sport for the fans by the fans. This is why teams have to have fan ownership and companies cannot buy naming rights to teams. The main exception to this rule has always been Bayer Leverkusen. Bayer never bought the naming rights to a Leverkusen based club as many would think. Instead Bayer established the club after 170 of its employees wrote to their employer asking for help establishing a sports club, mainly for gymnastics, to increase worker quality of life. Since then the club has been known as Bayer Leverkusen or a variation of the name.
Bayer bounced around the lower tiers of german soccer for the first 70 years of its existence. The club did not cement its place in the Bundesliga till the late 70's and even then struggled to find its footing. However, it quickly took off as a top tier club in the 80's, never winning the league but being surprisingly competitive for its lack of history.
In the 80's Bayer was in the top half of the table almost every season. Then they had their first huge victory as a club when they won the UEFA Cup (which is now known as Europa Cup) where they beat Espanyol coming down from 3-0 in the first leg. This is still a huge badge of honor for Bayer fans, to go from being a lower tier club to winning european metal in the span of 10 years is no easy challenge.
In the 90's Bayer picked up many great German players such as Ulf Kristen and Rudi Voller. After the huge infusion of quality into the club they won the Pokal in 1993 against lower tier amatuer Hertha Berlin. Unfortunately for Bayer, this is the last trophy they've won up to now. Their coach was fired a few years later in a cocaine scandal even while the team was beefing up its player talent, spending more money then German clubs had ever spent before. From 1997 to 2002 the team finished in the league second four times. One of these times BVB just raced ahead of them to take the league title. To make it even worse, Bayer lost the Pokal final and Champions league final, to go from potentially winning the first German Treble to taking nothing home at all. This is where the label Neverkusen comes from.
Culture and Fans:
Many fans of German football decry Bayer for being a plastic club. It is true that the BayArena tries to be more of a family atmosphere and less hostile then other stadiums. But Leverkusen is still a working class city and the Ultras at Leverkusen are as crazy as any you'd find anywhere else in the country. In fact the Bayer Ultras were the first to actually start calling themselves Ultras.
While the atmosphere may be no more crazy then that of the rich EPL teams like Arsenal or Man City, where expensive tickets are to blame for, there still is always a german flare to their fans way of celebrating as seen in the video below.
While the team may have a corporate name and majority owner it still, has the same Bundesliga feel we all know and love.