  A spate of remarkable new hadrons reported in 2003 may lead to unequivocal
proof of states beyond conventional $q\bar{q}$ and $qqq$ structure. Claimed
baryonic states Theta+, Phi, and Theta^0_c would consist of five quarks, and
new D_{sJ}-states and/or X(3872) might contain four quarks. I review efforts to
search for and study this ``new'' spectroscopy in pbarp-collisions with the CDF
II detector. Pentaquark searches are negative, and no evidence for exotic
analogs of D_{sJ}-states was found. CDF has confirmed the X(3872). My main
focus is the production and decay properties of the X(3872), and its possible
interpretations.
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