Solid state NMR signals are very sensitive to the local environment of the observed nucleus; however, their interpretation is not straightforward. On the other hand, first-principles DFT calculations of NMR parameters can now be applied to periodic compounds to predict NMR parameters. Thus, ab initio calculations can help to interpret the NMR spectra exhibited by complex materials, to assign NMR lines to structural environments, and even to enlighten the environmental factors influencing the NMR parameters for a given nucleus. Both techniques have been applied to crystalline compounds of the KF-YF3 binary system, -K3YF6, K2YF5, KYF4, -KY2F7 and -KY3F10, which present a variety of YFn and KFm polyhedra. First, the structure of K2YF5 was refined in the Pnma space group and, for all compounds, atomic positions were optimized by DFT. The F-19, Y-89 and K-39 NMR spectra have been recorded and the measured NMR parameters are compared to those calculated from the first-principles DFT method, allowing unambiguous assignments of NMR lines to crystallographic sites. Linear correlations between the experimental (iso) and calculated sigma(iso) values for the three nuclei are used to predict the theoretical F-19 spectra of KYF4 (24 F sites) and -KY2F7 (19 F sites) as well as the K-39 spectrum of KYF4 (6 K sites). For Y-89 and K-39, both computational and experimental results show a decrease of the isotropic chemical shift values when the cation coordination number increases. Above all, Y-89 isotropic chemical shift values correlate with the number of K atoms present in the Y second coordination sphere. For F-19, the combination of isotropic chemical shift and chemical shift anisotropy allows for distinguishing four kinds of F environments.