This review describes a series of studies on the Na+ superionic conducting glass-ceramics with Na5YSi4O12 (N5)-type structure synthesized using the composition formula of Na3+3x R-- y(1 -) xPySi3 (-) O-y(9) for a variety of rare earth elements, R, under the appropriate composition parameters. In the crystallization of N5 -type glass-ceramics, its relatives (Na3YSi3O9 (N3)- and Na9YSi6O18 (N9)-type glass-ceramics) structurally belonging to the family of Na24-3xYxSi12O36 were found to crystallize as the precursor phase at low temperatures. In order to produce N5 single phase glass-ceramics, the concentration of both phosphorus and rare earth was found important. The meaning of the composition was evaluated by kinetic study on the phase transformation of metastable N3 or N9 phases to stable N5 phase with Na+ superionic conductivity. The possible combinations of x and y became more limited for the crystallization of the superionic conducting phase as the ionic radius of R increased, while the Na+ conduction properties were more enhanced in the glass-ceramics of larger R. These results are discussed in view of the structure and the conduction mechanism. Also discussed were the microstructural effects on the conduction properties, which were dependent upon the heating conditions of crystallization. These effects were understood in relation to the grain boundary conduction properties as well as the transmission electron microstructural morphology of grain boundaries. Recent researches on structural control of the glass-ceramic Na+ superionic conductors are also introduced. The optimum conditions for crystallization were discussed with reference to the conduction properties and the preparation of crack free N5 -type glass-ceramics. The effects of Si substitution with the various elements with tetrahedral oxygen coordination structure and Y substitution with the various R elements were also discussed on ionic conductivity of N5 -type glass-ceramics, respectively. In addition, the results on control of the structure by bias crystallization of glasses in an electric field were presented. (C) 2015 Elsevier B.V. All rights reserved.