Webs of five-branes and N=2 superconformal field theories

We describe configurations of 5-branes and 7-branes which realize, when compactified on a circle, new isolated four-dimensional N=2 superconformal field theories recently constructed by Gaiotto. Our diagrammatic method allows to easily count the dimensions of Coulomb and Higgs branches, with the help of a generalized s-rule. We furthermore show that superconformal field theories with E6,7,8 flavor symmetry can be analyzed in a uniform manner in this framework; in particular we realize these theories at infinitely strongly-coupled limits of quiver theories with SU gauge groups.