Several experimental groups have reported evidence for baryons with flavor exotic quantum numbers that cannot be explained as $qqq$ bound states but require a minimum of five quarks -- $qqqq bar q$. These pentaquark states include the $theta^{+}$, the $Xi^{--}$ and the $theta_{c}$. The reported widths of these new states are consistent with experimental resolution and may be as narrow as a few MeV/$c^2$ or less. Prior to 2003, experimental searches for flavor exotic baryons spanning several decades yielded negative results. There have also been a number of searches carried out since the reports of these new pentaquark states that do not confirm their existence. This review of both the positive and negative reports seeks to understand the current situation regarding the experimental evidence for pentaquarks.