Self-oscillating biomechanical models of the vocal folds are indispensable tools for articulatory speech synthesis, speech coding, and speech analysis. A successful compromise between simplicity and completeness are the lowdimensional vocal fold models with lumped elements. This paper provides a survey of this class of models and compares them in terms of their mechanical design, aerodynamic simulation, and with respect to their application and evaluation. Future studies to improve the performance of these models in the context of articulatory speech synthesis will be proposed.