Asphalt has been widely used since 1920-1930, though in ancient times bitumen, the most important ingredient of asphalt, was already used for road-building. The advantage of asphalt over concrete is that it has a smoother surface. This means more comfort for drivers and less noise for the surroundings. Asphalt also tends to press into depressions and cracks over time, which makes it more suitable for an unstable foundation. In some countries where the soil is stable, it's quite common to build a road primarily of concrete, and then cover it with a thin layer of asphalt. In countries with a lot of peat and clay in the soil, however, only asphalt is used. The thickness of the asphalt layer is determined through calculation, for example by means of the Shell Pavement design method.
Concrete has superior strength and endurance, and will last longer. It is so strong that it can be very difficult to remove if the roadway needs to move, so it is typically only used on roads carrying very large loads on larger highways or main city roads. Concrete also tends to be noisy compared to a road covered in ashphalt, but new forms of concrete including small amounts of rubber can address this to some degree. The thickness of the concrete layer is also determined by calculation, the method varying by country and depending on whether steel reinforcement is used.
It is not uncommon to see bricks surfacing smaller roadways, notably in Europe. They have the advantage of easy removal and replacement, which is important because so much infrastructure is run under roadways. However, bricked surfaces are bumpy and so are suitable for low speed use only. Some see this as a positive effect of bricks, because it keeps people from speeding. For the thickness of bricks no calculation is done. For the thickness of sand under the bricks (or other materials), however, there are calculation methods, which also vary by country.
The majority of damage caused to pavement is due to heavy trucks (lorries). Few governments tax for this, however, as it would make shipping costs rise. Toll roads often take this into account, however, many including weighing stations to determine the toll. The damage by a truck is about 10,000 times more than by a normal car!