Modern nanoelectromechanical devices are used in a broad range of applications, including sensors for mass detection and imaging with atomic resolution, monitoring of biological processes such as DNA hybridization, and mass spectrometry at the molecular scale. These nanoscale devices are frequently operated in a fluid environment - both gas and liquid. The ability to model their behavior is essential for proper device design and characterization. While the Navier Stokes equations are used widely, and tools for their solution are well developed, this continuum treatment is often not applicable to flows induced by modern nanoscale devices. In this talk, I will give an overview of work in my group aimed at understanding oscillatory non-continuum flows at nanometer length scales and developing mathematical tools for their characterization. A particular emphasis will be placed on fluid-structure interactions at these length scales.