orbital resonances excited and ejected most of the asteroids.
Sometimes collisions between the many millions of asteroids alter their orbits to a more elliptical trajectory. After such a collision a few approach the Earth; they are called near-Earth asteroids. Even worse: some asteroids cross the Earth's orbit - these are the so-called Apollo asteroids. These Apollo asteroids are responsible for most of the impact events and most of the meteorites that have fallen on Earth. A very famous impact event was the Chicxulub event: the impact that caused the extinction of the dinosaurs and opened the way for some rat-like mammals to evolve within 'just' 65 million years to a species called Homo sapiens. The Chelyabinsk meteorite is the remnant of a very well-documented recent meteorite fall in 2013.
Comets are composed of ice, dust and rocky particles; that's why they are also called 'dirty snowballs'. They originate from outside Neptune's orbit. When they approach the Sun the solar radiation and solar winds cause a tail of particles which makes them visible in the night sky even to the naked eye. They orbit as long as all of their volatile material has evaporated away.
Don't miss our article about dwarf planets and and asteroids, meteoroids, meteors, meteorites and comets.