For several years, we have been developing and studying computer-simulated models of brass instruments, including the player's lips. We demonstrate here the most recent developments of our physical model, including physical functioning and real-time control with MIDI events. These improvements result in great improvements of sound quality and musical expressivity. To better understand the physics of real lips, we have built a working latex model of a pair of lips. We show that this artificial mouth can play a trumpet like a real trumpet player. We make comparisons between naturally blown trumpet signals, artificially-blown trumpet signals, and simulations with our computer model.