Dynamic simulation models of turbocharged Diesel and gasoline engines are increasingly being used for design and initial testing of engine control strategies. The turbocharger submodel is a critical part of the overall model, but its control-oriented modeling has received limited attention thus far. Turbocharger performance maps are typically supplied in table form, however, for inclusion into engine simulation models this form is not well suited. Standard table interpolation routines are not continuously differentiable, extrapolation is unreliable and the table representation is not compact. This paper presents an overview of curve fitting methods for compressor and turbine characteristics overcoming these problems. We include some background on compressor and turbine modeling, limitations to experimental mapping of turbochargers, as well as the implications of the compressor model choice on the overall engine model stiffness and simulation times.The emphasis in this paper is on compressor flow rate modeling, since this is both a very challenging problem as well as a crucial part of the overall engine model. For the compressor, four different methods, including neural networks, are presented and tested on three different compressors in terms of curve fitting accuracy, model complexity, genericity and extrapolation capabilities. Curve fitting methods for turbine characteristics are presented for both a wastegated and a variable geometry turbine.