They are perhaps the oldest remnants of the early Solar Sytem and what we learn from them tells us about our own early history. Most of the asteroids lie between the orbits of Mars and Jupiter, but some have very elliptical orbits which bring them very close to Earth. In number, there are probably billion of asteroids in the solar system. The largest known asteroid is Ceres which was the first asteroid to be discovered in 1801. It can be seen in amateur telescopes if one knows where and when to look.
Most asteroids are of the small irregular variety.
None of them are large enough to have high enough gravity to pull themselves into spherical shape. Images of the same asteroid vary in brightness which confirms the irregular shape. The Galileo spacecraft passed through the asteroid belt twice on its way to Jupiter. The spacecraft passed only 16.000 km from the asteroid Gaspra in 1990 and returned excellent images. Gaspra is an oblong world measuring 20 by 12 by 11 km.