We consider field theories arising from a large number of D3-branes ne
ar singularities in F-theory. We study the theories at various conform
al points, and compute, using their conjectured string theory duals, t
heir large N spectrum of chiral primary operators. This includes, as e
xpected, operators of fractional conformal dimensions for the theory a
t Argyres-Douglas points. Additional operators, which are charged unde
r the (sometimes exceptional) global symmetries of these theories, com
e from the 7-branes. In the case of a D-4 singularity we compare our r
esults with field theory and find agreement for large N. Finally, we c
onsider deformations away from the conformal points, which involve fin
ding new supergravity solutions for the geometry produced by the 3-bra
nes in the 7-brane background. We also discuss 3-branes in a general b
ackground.