Typically the questions I've been asked concerned whether significant quantities of hydrocarbon (oil or natural gas) would be found off of an area known as the Point (the Point is an area about 36 mi offshore of Cape Hatteras) and the potential environmental impacts of drilling in that area.
The oil companies have estimated that there is about a 7% chance of finding anything in the area and about a 2% chance of finding enough to be commercially worthwhile (it costs millions of dollars just to drill). Their interest in the area stems from the presence of a buried ancient reef deep below the seafloor. The reef, made of carbonate rock, is very porous and thus could hold large quantities of oil or gas. This same reef extends to the Gulf of Mexico where oil has been found. The area of the Point is also a high spot - if there is oil around it would most likely 'float up' to the high spot.
The problem is that the Point is home to abundant sea life (see the pictures in the powerpoint file). Though we are not entirely sure why, it is probably because the Gulf Stream from the south and the Virginia Current from the north converge in this area. In doing so, they bring together lots of food (phytoplankton, zooplnakton, etc) and different habitats (cold water, warm water) thus creating a biological hotspot.
The area will not be easy to drill in. The currents are strong, the seafloor is rugged and the region is prone to severe storms (it's not called the Graveyard of the Atlantic for nothing).
The process of producing oil is a long one. The first step is drilling exploratory wells. This initially is only one drilling using a special drill ship that can work in deep water (the water depth is 800 meters - about 1/2 mile). The water is too deep to anchor in so the ship stays in place with powerful thrusters. Mobil requested permission to do an exploratory drilling and was denied. Chevron started the process again but stopped when it became apparent the politics were not in their favor. I suspect there will be a revival in interest now.
If oil or gas is found, then more wells are drilled (about 10 plus or minus) to establish the size of the field. If it is determined that there is enough oil or gas to go after, then installation of permanent wells will begin. This whole process could take up to 10 years.
There would probably be a small environmental impact, if any, from the exploration phase unless a major (and unusual) accident occurred. The production phase, on the other hand, could an environment impact due to oil leakages and drilling spoils disposal.