Voiced speech is a highly complex process involving coupled interactions between the vocal fold structure, aerodynamics, and acoustic field. Reduced-order lumped-element models of the vocal fold structure, coupled with various aerodynamic and acoustic models, have proven useful in a wide array of speech investigations. These simplified models of speech, in which the vocal folds are approximated as arrays of lumped masses connected to one another via springs and dampers to simulate the viscoelastic tissue properties, have been used to study phenomena ranging from sustained vowels and pitch glides to polyps and vocal fold paralysis. Over the past several decades a variety of structural, aerodynamic, and acoustic models have been developed and deployed into the lumped-element modeling framework. This paper aims to provide an overview of advances in lumped-element models and their constituents, with particular emphasis on their physical foundations and limitations. Examples of the application of lumped-element models to speech studies will also be addressed, as well as an outlook on the direction and future of these models. (C) 2013 Elsevier B.V. All rights reserved.