  We explore the connections between three classes of theories: A_r quiver
matrix models, d=2 conformal A_r Toda field theories and d=4 N=2 supersymmetric
conformal A_r quiver gauge theories. In particular, we analyse the quiver
matrix models recently introduced by Dijkgraaf and Vafa and make detailed
comparisons with the corresponding quantities in the Toda field theories and
the N=2 quiver gauge theories. We also make a speculative proposal for how the
matrix models should be modified in order for them to reproduce the instanton
partition functions in quiver gauge theories in five dimensions.
