The Hellfire Club are responsible for some of the most iconic moments in X-Men history - Google "Wolverine Now It's My Turn" if you need a reminder - and have plagued the mutant team for decades as the secret society attempts to bend the world to their will. They're most notably responsible for helping to turn Jean Grey into Dark Phoenix, while X-Men member Emma Frost was a pivotal part of the organisation for a time. They haven't been up to an awful lot in recent years, and while a youthful Hellfire Club was recently formed which took on the Jean Grey School in Wolverine and the X-Men, they didn't have too much of an impact. However, with a TV show on the way (which sounds like it pick up with the organisation before the events of X-Men: First Class), don't be surprised to see their presence in the Marvel Universe increase greatly.
