Radio Controlled or R/C vehicles are generally 1:10 scale models which simulate or approximate existing automobiles, boats, helicopters, airplanes, motorcycles, tanks, and other vehicles. Due to the square-cube law they can perform feats which would utterly destroy their 1:1 scale counterparts. It is possible to make a full-scale vehicle remote controlled, and in fact this is done on a regular basis, for example to land certain "high-tech" aircraft in the case of pilot incapacitation.
Generally speaking, most radio controlled vehicles use a multiple-channel AM (amplitude modulated) or FM (frequency modulated) analog radio signal, though PCM (pulse code modulated) radio has gained popularity in more recent years due to its falling cost and generally more reliable signal. In almost every case, the radio system consists of a transmitter which may also receive signals from the remote end in the case of more expensive radio sets, a receiver, and one or more servos. R/C servos are pulse rate controlled, meaning sending them a higher frequency pulse on their control line (they also have power and ground connections) will make them turn further. Other R/C devices such as speed controllers mimic a servo (to the radio receiver's view) in that they take the same signal as a servo, but they have no moving parts.
Radio controlled helicopters, like real helicopters, use a gyroscope for stabilization. These "gyros" take servo signals (used for collective and/or pitch) in, and output a faster or slower signal to compensate for motion.
In general radio controlled vehicles range from about 1:4 scale (for large gas-powered vehicles) down to the tiny "Bit Char-G" and similar cars which are about an inch and a half long, though there are numerous 1:2 scale tanks and such out being driven around. The most common scale is 1:10, which produces cars in the neighborhood of 12 to 16 inches in length. These vehicles are capable of traveling up to about 35mph for electric and 70mph for gasoline or nitro-powered, though going that fast with wheels 1/10 of their normal diameter can be difficult at best. Wheeled R/C racing is generally done on tarmac which has been well-swept and sprayed with sugar water in order to make it sticky, since these vehicles are not large enough to have meaningful downforce.
Off-road R/C cars and trucks are certainly more versatile in that they can run on a variety of surfaces. Some particularly well-sealed and filtered cars and trucks can even run on sand, though in general the beach is the worst place for anything with moving parts, as sand is quite hard, and comes in a wide variety of abrasive sizes and shapes. In general, the best place to race these vehicles is on dirt or very short and loose grass, which is slightly moist to minimize dust. Some hobby shops run broad, well-maintained and leveled tracks, but racing on rough backyard tracks is exciting in a different way; You don't go as fast, but you really learn to handle the rough terrain.
Most radio controlled cars come preassembled and there is little or no price benefit from purchasing them as an unassembled kit. While for many years only cheap cars (such as those which go forward, or backwards in reverse all the time) came completely preassembled, and it was generally necessary to purchase a R/C car as a kit, and purchase a radio kit and motor separately. Now, the vast majority of higher-end vehicles now ship "ready to run" (R2R/RTR) with a radio rig and motor included. You simply glue the tires to the wheels (otherwise they will fall off during hard corering) using CA Glue, also known as cyanoacrylate or super glue, and when it dries you may install the wheels and drive the car. R/C vehicles with internal combustion engines require a break-in period, following the same principles as an actual auto. Generally running through two tanks of fuel at no more than half throttle is enough to break them in at which time you get to go through the joy of tuning a two-stroke engine with a very small carburetor.
Full-scale vehicles are occasionally controlled via radio for the purpose of stunts which cannot be engineered to be survivable by a driver, or simply for the entertainment of enthusiasts.