My recent work on integrable structure of melting crystal models is reviewd. The simplest model is a statistical model of random 3D Young diagrams. A variant of this model originates in topological string theory on the resolved conifold. These two models are related to the 1D Toda hierarchy and the Ablowitz- Ladik hierarchy, respectively. These results can be further extended to ``orbifold'' models. The relevant integrable systems are particular reductions of the 2D Toda hierarchy.