In this paper we describe tunable interference filters based on arrays of MEMS micromirrors. A simple analytical description of the height distribution of micromirrors needed to create a desired spectral response is presented, and the implications on the design and utility of MEMS interference filters are discussed. Finally we describe two practical filter implementations. The first enables continuous spectral control over relatively broad bands, and the second is designed for Wavelength-Division-Multiplexed fiber optic communication systems.