The present invention relates to a crushing device comprising a jaw crusher provided with two jaws, at least one jaw of which moves reciprocally toward the other jaw and away from the other jaw in use, a supply device for supplying material to be crushed to the jaw crusher and a discharge device for discharging crushed material. The crushing device comprises a housing that encloses the jaw crusher, a ventilation device provided with air outlet openings that open into the crushing space, by means of which ventilation device air can be blown under pressure between the jaws of the jaw crusher device, and an exhaust device, which exhausts air mixed with fine material produced by the jaw crusher from the housing. The exhaust device is configured to convey the fine material mixed with the air to a collecting location. The invention further relates to a method for crushing material by means of such a crush device.