We discuss the field theory of 3-brane probes in F-theory compactifications in two configurations, generalizing the work of Sen and of Banks, Douglas and Seiberg. One configuration involves several parallel 3-brane probes in F-theory compactified on $T^4/Z_2$, while the other involves a compactification of F-theory on $T^6/Z_2 x Z_2$ (which includes intersecting $D_4$ singularities). In both cases string theory provides simple pictures of the spacetime theory, whose implications for the three-brane world-volume theories are discussed. In the second case the field theory on the probe is an unusual N=1 superconformal theory, with exact electric-magnetic duality. Several open questions remain concerning the description of this theory.

havmac, 24 pages, no figures; revised version; we have corrected the discussion concerning the relationship between the orientifolds and the F-theory compactification. Version to be published in Nucl. Phys. B