In magnetic resonance imaging (MRI) the raw data is measured in k-space, the domain of spatial frequencies. Methods that use a non-Cartesian sampling grid in k-space, e.g. a spiral, are becoming increasingly important. Reconstruction is usually performed by resampling the data onto a Cartesian grid and the usage of the standard FFT - often denoted by gridding. Another approach, the inverse model, is based on an implicit discretisation. Both discretisations are solved efficiently by means of the NFFT and the inverse NFFT, respectively. Furthermore, a unified approach to field inhomogeneity correction has been included, see [33,17] for details.