Gaspra, in a picture taken by Galileo spacecraft in 1991 - U.S. Geological Survey

Main Belt

Asteroids are metallic, rocky bodies without atmospheres that orbit the Sun but are too small to be classified as planets, so they are also known as “minor planets”.
They are in groupings in different Solar system areas and receive these names:

Near Earth Asteroids (NEAs)
Main Belt
Trojans
Centaurs*

Tens of thousands of asteroids congregate in the so-called Main Belt: a vast, doughnut-shaped ring located between the orbits of Mars and Jupiter from approximately 2 to 4 AU. Inside the belt, the asteroids concentrate on sub-groups named after the main asteroid of each one: Hungarias, Floras, Phocaea, Koronis, Eos, Themis, Cybeles and Hildas.
Between the main concentrations of asteroids in the Main Belt are relatively empty regions known as the Kirkwood gaps. These are regions where an object's orbital period would be a simple fraction of that of Jupiter. An object in such an orbit is very likely to be accelerated by Jupiter into a different orbit.

Asteroids are thought to be primordial material prevented by Jupiter's strong gravity from accreting into a planet-sized body when the solar system was born 4.6 billion years ago. It is estimated that the total mass of all asteroids would comprise a body approximately 1,500 kilometers in diameter, less than half size of the Moon.
Known asteroids range in size from Ceres, the largest, at about 960 km in diameter down to the size of Pebbles with less of 1 Km. (See Comparative) Sixteen asteroids have diameters of 240 Km or greater. The majority of main belt asteroids follow slightly elliptical, stable orbits, revolving in the same direction as the Earth and taking from three to six years to complete a full circuit of the Sun.

Asteroids, according to their chemical composition, are classified into 3 types:

C-type (carbonaceous)

Includes more than 75 percent of known asteroids. Very dark with an albedo of 0.03 - 0.09. Composition is thought to be similar to the Sun, depleted in hydrogen, helium, and other volatiles. C-type asteroids inhabit the main belt's outer regions.

S-type (silicaceous)

Accounts for about 17 percent of known asteroids. Relatively bright with an albedo of 0.10 - 0.22. Composition is metallic iron mixed with iron- and magnesium-silicates. S-type asteroids dominate the inner asteroid belt.

M-type (metallic)

Includes many of the rest of the known asteroids. Relatively bright with an albedo of 0.10 - 0.18. Composition is apparently dominated by metallic iron. M-type asteroids inhabit the main belt's middle region.

Meteoroids, Meteorites and Meteors

The relationship between asteroids and meteoroids is still in debate, like explain bellow, but in general it is believed that these last ones are fragments of those and they also can be fragments of comets. The periodic rains of meteors like the Orionides and Draconides, happen when the Earth goes by the orbit of a comet (see Comets). The fragment of a meteoroid that is able to cross the atmosphere and hit the Earth or any other body in the space, it is denominated Meteorite, and those that don't arrive are Meteors.

The most common meteorites, known as ordinary chondrites, are composed of small grains of rock and appear to be relatively unchanged since the solar system formed. Stony-iron meteorites, on the other hand, appear to be remnants of larger bodies that were once melted so that the heavier metals and lighter rocks separated into different layers.

A long-standing scientific debate exists over whether the most common asteroids (the S-types) are the source of ordinary chondrites. Spectral evidence so far suggests that the S-type asteroids may be geochemically processed bodies akin to the stony-irons. If S-types are unrelated to ordinary chondrites, then another parent source must be found. If the two are related, then scientists need an explanation for why they aren't spectrally similar.

Main Belt objects represented in 3D models

Ceres as seen by Hubble Space Telescope – HST – NASA

1 Ceres (Dwarf Planet)

The smallest in those now denominated Dwarf Planets, (Eris and Pluto precede him) and although it no longer belongs to the asteroids category, it is the largest Main Belt object by far, it is C type with 933 km in diameter, the only asteroid practically spherical, and contains about 25% of the mass of all the asteroids combined. Was the first discovered asteroid in 1801. Currently underway is "Dawn" NASA mission to explore Ceres in August 2015.
(see more information - see data sheet)

Full View of Vesta
This mosaic synthesizes some of the best views that "Dawn" had of the giant asteroid Vesta
Image Credit: NASA/ JPL-Caltech/ UCLA/ MPS/ DLR/ IDA

4 Vesta

It has spheroid shape with 530 km in diameter, the third larger known. Recently it has been detected that it is compound in layers stratified as the terrestrial planets, for what is thought that it should possess some internal source of heat. Currently underway is "Dawn" NASA mission that explored Vesta October 2011 to May 2012 and will visit Ceres in August 2015.
(see data sheet)

Mathilde, photographed by NEAR-Shoemaker in 1997 - Near Earth Asteroid Rendezvous Mission

253 Mathilde

Is a main belt asteroid with a relatively small perihelion (1.94 AU) Mathilde is our first look at a C-type. Another oddity is that Mathilde's rotation rate is very slow, 17.4 days. It is one of the five asteroids visited up to now by some spacecraft.** It has at least 5 great craters bigger than 20 kilometers in diameter, and that represents a puzzle, since is not explanation some of how craters of that kind can take place in such a small body and it can subsist to such impacts.
(see data sheet)

Ida & Dactyl, photographed by Galileo spacecraft - NASA – JPL

243 Ida

Smaller than Mathilde, with 58 x 23 km and Koronis' family member, is another of the only four asteroids visited by a spacecraft. The Galileo ship went by Ida in its trip to Jupiter in 1993, and in the pictures sent to Earth, surprisingly was discovered the first moon around an asteroid; Dactyl, of 1.6 x 1.2 km, orbiting to 90 km of Ida.
Ida's composition is a quiz, since it seems to be Type S, and there are evidences that it contains some magnetic material, but its density is as low as the asteroid Type C, and it doesn't correspond with density of the iron asteroids and stony-iron ones as to have a magnetic field.
(see data sheet)

* Although now it is known that the Centaurs are more similar to the Kuiper Belt objects and Comets nucleus (treaties in another SISV chapter) they are continued considering Asteroids.
** The five visited asteroids are: Gaspra (1991) and Ida (1993) by Galileo spacecraft, Mathilde (1997) and Eros (2001) by NEAR-Shoemaker and Vesta (2011-2012) by Dawn spacecraft. Ceres is also in process of being visited by Dawn in August 2015.

Information compiled from NASA Solar System Exploration Planets, Bill Arnett's Nine-now-eight Planets, WIKIPEDIA and NASA Dawn mission site.