All of the modern road brakes are an adaptation of the caliper type.
Single pivot side-pull
Single pivot side-pull caliper brakes consist of two curved arms that cross at a pivot above the wheel
and hold the brake pads on opposite sides of the rim.
These arms have extensions on one side, one attached to the cable, the other to the cable housing. When the brake lever is squeezed, the arms move together and the brake pads squeeze the rim.
These brakes are simple and effective for relatively narrow tires,
but have serious disadvantages if made big enough to fit wide tires.
Low-quality varieties also tend to rotate to one side during actuation and to stay there, so that one brake pad continually rubs the rim
even when the brake is released. These brakes are now used on inexpensive bikes; before the introduction of dual-pivot caliper brakes they were used on all types of road bikes.
Centre-pull caliper brakes have symmetrical arms and by design do not rub the rim
when they are released, by actuating the brake arms symmetrically. The cable housing attaches to a fixed cable stop attached to the frame,
and the inner cable attaches to a sliding piece or a small pulley,
over which runs a straddle cable connecting the two brake arms. Tension on the cable is evenly distributed to the two arms, preventing the brake from taking a "set" to one side or the other. These brakes were reasonably priced, and in the past filled the price niche between the cheaper and the more expensive models of side-pull brakes.
Dual-pivot caliper brakes are used on most modern racing bicycles. One arm pivots at the centre, like a side-pull; and the other pivots at the side, like a centre-pull. The cable housing attaches like that of a side-pull brake; the centering of side-pull brakes was simplified with the mass-market adoption of dual-pivot side-pulls (an old design re-discovered by Shimano in the early 1990s). These brakes offer a higher mechanical advantage. Dual-pivot brakes are slightly heavier than conventional side-pull calipers and cannot accurately track an out-of-true rim.