The importance of exploring new solid electro-lytes for all-solid-state batteries has led to significant interest in NASICON-type materials. Here, the Sc3+-substituted NASICON compositions (NaScZr2-x)-Sc-3-Zr-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 Na-23, P-31, and Si-29 nuclear magnetic resonance (NMR) spectroscopy. A phase transition between 295 and 473 K from monoclinic C2/c to rhombohedral R (3) over barc is observed for the N3 compositions, while N2 compositions crystallize in a rhombohedral R (3) over barc unit cell in this temperature range. Alternating current (AC) impedance spectroscopy, molecular dynamics (MD), and high temperature Na-23 NMR studies are in good agreement, showing that, with a higher Sc3+ concentration, the ionic conductivity (of about 10(-4) S/cm at 473 K) decreases and the activation energy for ion diffusion increases. Na-23 NMR experiments indicate that the nature of the Na+-ion motion is two-dimensional on the local atomic scale of NMR although 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 ions between Na(1) and Na(2) sites.