Pentaquarks: Facts and puzzles

On the occasion of the celebration of the 70th birthday of Prof. Yu.A. Simonov, we contribute a brief review of the status of exotic baryons, which are most likely pentaquark states. We summarize the experimental status of exotic baryons, discuss the baryon antidecuplet to which exotic baryons possibly belong, and review theoretical expectations for the masses and widths of recently discovered {theta} and {xi}{sub 3/2} baryons which have come from studies of QCD sum rules, lattice QCD, and quark models. We also pay special attention to the dynamical calculation of pentaquark masses in a framework of the QCD string approach originally elaborated by Simonov for baryons and using the Jaffe-Wilczek [ud]{sup 2}q-bar approximation for the pentaquark states.