We present several new examples of non-trivial 4D N = 1 superconformal
field theories. Some of these theories exhibit exotic global symmetri
es, including non-simply laced groups (such as F-4) They are obtained
by studying three-brane probes in F-theory compactifications on ellipt
ic Calabi-Yau threefolds. The geometry of the compactification encodes
in a simple way the behavior of the gauge coupling and the Kahler pot
ential on the Coulomb branch of these theories.