Disc brakes are the preeminent choice for all automobile manufacturers. Even those employing drum brakes in the back will invariably have disc brakes in the front. In short, this type of brake system is superior in terms of design and essentially operates like a drum brake turned inside out. This type of brake system is most likely what you have on your current vehicle.
High performance vehicles with higher speeds need better brakes to slow them down, so you'll likely see disc brakes on the rear of those too. Disc brakes are again a two-part system. Instead of the drum, you have a disc or rotor, and instead of the brake shoes, you now have brake caliper assemblies. The caliper assemblies contain one or more hydraulic pistons which push against the back of the brake pads, clamping them together around the spinning rotor. The harder they clamp together, the more friction is generated, which means more heat, which means more kinetic energy transfer, which slows you down. You get the idea by now.
Disc brake systems work by using hydraulic pressure to press a pad against the rotor to slow the vehicle. When the brake pedal is pressed, it acts upon the piston in the master cylinder which sends pressure via the brake lines to the caliper. The pad-to-rotor friction stops the wheel from turning.
Because a disc brake assembly can absorb more heat than a drum brake assembly, most cars use disc brakes for their front brake systems. When the brake pedal is pushed, brake fluid from the master cylinder compresses the brake pads against the rotors attached to the vehicle's front wheels. The friction between the stationary pads and the revolving rotors causes the rotors and wheel to slow and stop.