Microfluidics offers unprecedented avenues for controlling and characterizing the behavior of physical, chemical, and biological systems.  However, in order to leverage the full potential of microfluidic devices as measurement tools, the community requires a deeper theoretical understanding of how they operate.  Our current research addresses this problem by developing and analyzing mathematical models of such systems.  We use a variety of approaches -- applied analysis, asymptotics, numerical methods, and optimization -- to understand how such models can be used as the basis for measuring properties of particles and other systems in flow.  We also work closely with experimentalists in the Physical Measurement Laboratory to develop new microfluidic devices and measurement tools, and to validate our mathematical approaches.