The main Belt

Most of the asteroids in the solar system inhabit the main asteroid belt, orbiting the Sun between Mars and Jupiter, between 2 and 3.3 AU, with a few stragglers beyond this zone (at 4 AU). 
The discovery of the first main-belt asteroid (Ceres, in the year 1801) was first seen as a confirmation of the Titus Bode's empirical law, which had foreseen the presence of an unseen planet at 2.8 AU. From that moment many other asteroids have been discovered (in order, Pallas, Juno, Vesta etc), and scientists began to call this zone of concentration the Main Belt. Nowadays, more than 10000 objects have been discovered but the exact number of asteroids in the Main Belt is still unknown: for what concerns asteroids bigger than 1 Km, previsions range from 100000 up to a million objects (click here to know more about the history of asteroid's science).
The orbits of these main belt asteroids are generally stable, and in a first approximation, thy can be thought to be regular and elliptical, following the classical Kepler's Formula. In the reality these orbits are not perfectly circular, and are inclined on the plane where the solar system lies.

Moreover, for the gravitational influences of Mars and Jupiter, the orbits are not uniformly distributed over the main belt where some relatively empty regions, called Kirkwood gaps, exist.
These main belt asteroids have passed through periods of heavy bombardment, and while a few of them have grown in size (as Ceres), the smaller ones have experimented collisional fragmentation (click here to know more about the primordial solar system). After every collision, the newly formed asteroids which have started moving independently but with similar orbits, can be grouped in what are called the Hirayama families .
Furthermore, main belt asteroids, being close to the sun, were formed quite hot, and so the high temperatures vaporized the lighter substances, such as water, leaving a characteristic chemical composition made of mostly silicates, carbon and metals (click here to know more about the chemical classification of asteroids).

Kirkwood gaps

Asteroids of the main belt do not cover uniformly the area of the main belt. The regions which seem to be empty of objects are called Kirkwood gaps and can be easily explained by the near-by presence of Jupiter and the mechanism of resonance. If an asteroid in the main belt is in "resonance" with Jupiter, it means that it has a period that corresponds to a fraction of the period of Jupiter. For these asteroids the gravitational attraction of Jupiter is maximum, and so they are pretty soon cleared out from that orbit, which falls in a Kirkwood gap. On the other hand, if an asteroid has an orbit that is not in resonance, it will be affected by Jupiter but in random (casual) intervals, so that on an overall long time, the influence of Jupiter on its orbit is practically null. (Click here to know more about the mechanism of resonance and its consequences)

To visualize the presence of the gaps in the main belt it is possible to trace this histogram where the number of asteroids in the main belt is plotted as a function of the orbit's major semiaxis a (click here to know more about the parameters that identify an orbit) .
In this histogram, the inner and outer limits of the main belt are clearly visible (at 2.0 and at 3.2 AU) as well as the Kirkwood gaps that lie in this area. The outer zones of concentration of asteroids are also visible.

Hirayama families

The Hirayama family are groups of asteroids that travel in a cluster along the same orbit. They are probably remnants of a single, large body that was broken into a group of smaller asteroids. The principal Hirayama families are Hungarias, Floras, Phocaea, Koronis, Eos, Themis, Cybeles and Hildas (which are named after the main asteroid in the group).

In this graph it is possible to see the distribution of the main belt asteroids as a function of their major semiaxis a and of the inclination of their orbit (click here to know more about the parameters as a and sin (i) that identify an orbit). Some very evident concentratons of asteroids are visible in the graph. In particular the three most evident concentrations on the right of the plot are the Themis, Eos and Koronis families.