Auditory filter models have a history of over a hundred years, with explicit bio-mimetic inspiration at many stages along the way. From passive analogue electric delay line models, through digital filter models, active analogue VLSI models, and abstract filter shape models, these filters have both represented and driven the state of progress in auditory research. Today, we are able to represent a wide range of linear and nonlinear aspects of the psychophysics and physiology of hearing with a rather simple and elegant set of circuits or computations that have a clear connection to underlying hydrodynamics and with parameters calibrated to human performance data. A key part of the progress in getting to this stage has been the experimental clarification of the nature of cochlear nonlinearities, and the modelling work to map these experimental results into the domain of circuits and systems. No matter how these models are built into machine-hearing systems, their bio-mimetic roots will remain key to their performance. In this paper we review some of these models, explain their advantages and disadvantages and present possible ways of implementing them. As an example, a continuous-time analogue CMOS implementation of the One Zero Gammatone Filter (OZGF) is presented together with its automatic gain control that models its level-dependent nonlinear behaviour.