In the Gulf of Maine, some extreme fishermen go after blue sharks with chum flies. The fish are worked up into a frenzy like Adrian talked about, and then a big, fleshy looking fly (5/0, about 10" long) is thrown into the mix and dead drifted until Mr. Shark comes along and chomps down. Most of these blues are small (under 4 feet) and are easily handled on a 9 to 11 weight outfit.
There were a couple of daring souls who tried to get a mako on a fly. Same situation as the blue sharks, a huge (8/0, about 14" long) chum fly was used, but the makos don't take to the chum as readily as the blues. In fact, the sometimes come to the chum slick to feed on the small blue sharks that are there! And makos are much larger, measuring hundreds of pounds and catapulting out of the water during a fight on conventional tackle, so I can't imagine what would have happened if those guys had connected with their 12 weight.
Talk about grabbing a bull by the horns.