New medicines are usually tested first in human tissue, then on mice, and finally on humans. To oversimplify a bit, the first checks if it will do the job, while the second checks if it could have side-effects in other organs. As to why monkeys are not used instead of mice, (1) they take longer to grow up, (2) they are more expensive to maintain, and (3) experimenting on monkeys is considered more of a bad thing than experimenting on mice.