The story of Burtram is a common one in the beginning. Denied his rightful share of his father fortune Burtram went to his brother, Warren Jr. to borrow money which he used to buy a secret base under the Statue of Liberty that would be the headquarters of his illegal diamond smuggling operation.
Before we can move on we must stop to examine the brilliance of this plan. Because it is a common tourist location no one will notice a few extra people. As an island it is possible for ships to dock without going through typical channels so the chances of getting caught are far less and most importantly you can turn the statue of liberty into a giant remote control weapon of destruction. (So far as I know Dazzler did not do this but it can only be because of time management issues).
His ultimate plan was to create a giant laser using the diamonds. This laser called the Spatial Destructor(You have to give him style points for the name). Saddly before he could create this ultimate weapon his meddling brother(upon finding secret base under statue of liberty on the expense report) discovered what he was doing.
Dazzler, smart enough to stay out of these things himself, hired goons to kill his brother(Using the money he borrowed from his brother presumably).
Warren Worthington III, AKA. Angel learned of his fathers death and immediately assumed that it was Burtran Worthington and sought vengeance.
Using the teleporter he had in the base(No need to explain that every secret base has a teleporter) Dazzler imprisoned Angel in a room with his girlfriend Candy Southern. He then attempted to brainwash Angel to steal him a diamond big enough for his machine. This failed because Angel is a mutant and no mutant can ever be mentally controlled. (Never, none of them. It's a known fact all other examples are simply misunderstandings or possibly the placebo effect.)
With the help of several other X-men Angel was able to defeat a middle aged man with a half completed laser and Dazzler was put in prison. As this did not appear to be enough punishment for Angel he later suggested the name Dazzler be given to Alison Blaire as a constant reminder to his uncle of his disdain for the man. This is still Alison Blaire's primary reason for remaining with the X-men.
Burtram has not returned to crime mostly due to his inability to come up with a name cooler than Dazzler though he was recently overheard asking a friend what he thought of the name Lazeler so his criminal tenancies may be returning.