From http://jove.geol.niu.edu/faculty/fischer/105_

This is a kimberlite pipe. If you find one of these, you may have hit gold! Well, diamonds...

Diamonds are very hard to bring to the surface. For being such a hard substance, they seem so delicate! In order for a diamond to maintain its crystalline structure, it needs to come up to the surface fast. If it's brought up too slow, it will turn into graphite (for anyone who owns a push pencil, they'd know how valuable this can be!). So how, you might ask, do diamonds come to the surface? Through volcanic eruptions, at roughly 10 to 30 km/hour (and as it approaches the surface, this speed increases to supersonic speeds)(socrates.berkeley.edu/~eps2/wisc/Lecture6.html, 2004)! These volcanoes are known as kimberlite volcanoes. The rocks where the majority of diamonds are found are called kimberlite, and the term kimberlite pipe refers to the tubes of diamond-speckled rock. What's all this talk about kimberlite?

Well, kimberlite is an igneous rock that is rich in olivine and sometimes contains diamonds. Lamproite is also a rare igneous rock that is high in olivine and sometimes diamonds too. It is rare for a metamorphic rock to have diamonds, as they'd have to form deep within the earth.

There is one exception to where diamonds form. Sometimes they can form on the surface of the earth! And no, I don't mean fake ones in some laboratory that some cheap guy buys his girlfriend trying to play it off as real. This is done through meteorite impacts, as they can sometimes get the right amount of pressure and temperature (Gems and Precious Stones lecture, 2003). However, this is very rare.