Principles used when constructing models for velocity spectra are reviewed. Based upon data from the Kansas and Minnesota experiments, simple spectral models are set up for all velocity components in stable air at low heights, and for the vertical spectrum in unstable air through a larger part of the planetary boundary layer. Knowledge of the variation with stability of the (reduced) frequency f, for the spectral maximum is utilized in this modelling. Stable spectra may be normalized so that they adhere to one curve only, irrespective of stability, and unstable w-spectra may also be normalized to fit one curve. The problem of using filtered velocity variances when modelling spectra is discussed. A simplified procedure to provide a first estimate of the filter effect is given. In stable, horizontal velocity spectra, there is often a ‘gap’ at low frequencies. Using dimensional considerations and the spectral model previously derived, an expression for the gap frequency is found.