Summary: This paper deals with the nonlinear models of regenerative chatter on machine tools. The limitations and actual problems of the existing theory are summarized. These cause difficulties in industrial applications, like in the design of optimum technological parameters, adaptive control and/or vibration-suppression strategies. An industrial machine-tool vibration case is analysed experimentally and conclusions are drawn with respect to the likely mechanism of the nonlinear behaviour in a four-dimensional phase-space representation embedded in the infinite-dimensional phase space of regenerative chatter. In some respects, the whole phenomenon seems to be analogous to the turbulence in fluid mechanics.