  We develop tools for determining the gauge theory resulting from a
configuration of Type IIB D3-branes probing a non-compact, toric Calabi-Yau
3-fold, in the presence of additional flavor D7-branes with general embeddings.
Two main ingredients of our approach are dimer models and mirror symmetry.
D7-branes with general embeddings are obtained by recombination of elementary
D7-brane constituents. These tools are then used to engineer a large set of
Bipartite Field Theories, a class of 4d, N=1 quantum field theories defined by
bipartite graphs on bordered Riemann surfaces. Several explicit examples,
including infinite families of models, associated to both planar and non-planar
graphs are presented.
