The importance of exploring new solid electrolytes for all-solid-state batteries has led to significant interest in NASICON-type materials. Here, the Sc3+-substituted NASICON compositions Na3ScxZr2-x(SiO4)2-x(PO4)1+x (termed N3) and Na2ScyZr2-y(SiO4)1-y(PO4)2+y (termed N2) (x, y = 0 – 1) are studied as model Na+-ion conducting electrolytes for solid-state batteries. The influence of Sc3+ substitution on the crystal structures and local atomic environments has been characterized by powder X-ray diffraction (XRD) and neutron powder diffraction (NPD), as well as solid-state 23Na, 31P, and 29Si nuclear magnetic resonance (NMR) spectroscopy. A phase transition between 295 and 473 K from monoclinic C2/c to rhombohedral R c is observed for the N3 compositions, while N2 compositions crystallize in a rhombohedral R c unit cell in this temperature range. Alternating current (AC) impedance spectroscopy, molecular dynamics (MD) and high temperature 23Na NMR are in good agreement, showing that with a higher Sc3+ concentration, the ionic conductivity (about 10-4 S/cm at 473 K) decreases and the activation energy for ion diffusion increases. 23Na NMR experiments indicate that the nature of the Na+-ion motion is two-dimensional on the local atomic scale of NMR though the long-range diffusion pathways are three-dimensional. In addition, a combination of MD, bond valence, maximum entropy/Rietveld and van Hove correlation methods has been used, to reveal that the Na+-ion diffusion in these NASICON materials is three-dimensional and that there is a continuous exchange of sodium between Na(1) and Na(2) sites.