Heterogeneous multiscale method (HMM) is a general framework for linking different physical models at different scales. It is based on a top-down philosophy and it is a data-driven coupling method, i.e. it starts with a macroscale solver and the missing data in the macroscale solver are estimated using constrained microscale models. This framework has proven to be very effective for a wide variety of applications. We will discuss the basic principles behind HMM, as well as applications to modeling polymeric fluids and liquid crystal flows, modeling fluid-solid interactions at the interfaces and stochastic simulation algorithms for chemical kinetic systems with disparate rates.

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