It depends a bit on which "time era" you look at, in the SW universe.
Right after Order 66, where the clone army is being redone into the Imperial Army, they are all clones. Not all are Kamino made clones though, because they take too long to make. The new type of clones are Spaarti clones, which are full-grown within a year. They are usually less capable than the Kamino versions.
Later on, the stormtrooper corps accept human recruits as well, so you get a mix of clones and human. this creates other problems, as humans are not as well trained and are more exposed to act on feelings.
Eventually, in the New Jedi Order era, the Empire Remnant accept aliens into the ranks of the 501st. Now they look more at capabilities of the recruits.
All this is just from the top of my mind, remebering what I've read in the novels.
the Republic Commando/Imperial Commando books "Order 66" and "501st" by Karen Traviss covers the first era that I mentioned.
The short story of Davin Felth, in the book "Tales from Mos Eisley Cantina" covers humans into the ranks.
Timothy Zahn wrote a book where Mara Jade came in contact with troopers from 501st, which squad icluded an alien. The same book also had a short story with the 501st, covering how that alien got recruited. I don't remember the name of that book...