Recent experimental and theoretical investigations on a variety of yttria-stabilised zirconia (YSZ) nanomaterials are reviewed. The investigations were conducted within the frame of a collaboration of three institutions: (i) Charles University in Prague, (ii) Helmholtz Centre Dresden-Rossendorf and (iii) Donetsk Institute for Physics and Engineering of the NAS of Ukraine, Materials studied involved pressure-compacted nanopowders of binary and ternary (with Cr2O3 additive) YSZ and YSZ ceramics obtained by sintering the nanopowders. The nanopowders were prepared by the co-precipitation technique. Positron annihilation spectroscopy including the conventional positron lifetime (LT) and coincidence Doppler broadening (CDB) techniques was employed as the main experimental tool. Slow positron implantation spectroscopy (SPIS) was used in investigation of commercial YSZ single crystals for reference purposes. Extended state-of-art theoretical ab-initio calculations of positron response in the ZrO2 lattice were carried out for various vacancy-like defect configurations. It was suggested by these calculations that none of the oxygen-vacancy related defects are capable to trap positrons. On the other hand, zirconium vacancy was demonstrated by the calculations to be a deep positron trap, even in the case that a hydrogen atom is attached to the vacancy. The measured positron LT data clearly indicated that positrons annihilate in nanopowders predominantly from trapped states at defects of two kinds: (a) the vacancy-like misfit defects concentrated in layers along the grain boundaries and characterised with lifetimes of 0.180 ns, and (b) the larger defects of open volume comparable to clusters of a few vacancies which are situated at intersections of three (or more) grain boundaries (characteristic lifetimes of 0.380 ns). The intensity ratio of LT components corresponding to these two kinds of defects was found to be correlated with the mean particle size. This correlation reconfirms the above interpretation of LT components and, moreover, the measured ratios could be used to estimate changes of the mean particle size with chromia content or sintering temperature. It was shown in this way that chromia addition to the YSZ nanopowder leads to a smaller particle size compared to the binary YSZ. Similarly, grain growth during sintering could be monitored via this intensity ratio. A portion of 10 % of positrons was found to form positronium (Ps) in compacted binary YSZ nanopowders. The observed ortho-Ps lifetimes correspond to Ps pick-off annihilation in cavities of 3 nm size which may be expected to occur between the primary nanoparticles. On the other hand, an addition of chromia at a concentration as low as 0.3 mol.% appeared to be sufficient to suppress Ps formation below the detection limit. Similarly, Ps formation could not be detected in binary YSZ sintered for 1 hour at a temperature of 1000 °C or higher. The former effect indicates an enhanced concentration of Cr cations at the particle surfaces, while the latter one appears to be due to a decrease of cavity concentration induced by sintering. The measured CDB data supported the idea that vacancy-like trapping centres are similar to zirconium vacancies and gave further evidence of a strong segregation of Cr segregation at particle interfaces. SPIS was further involved in a trial experiment on binary YSZ nanopowders and sintered ceramics. This experiment clearly demonstrated that SPIS may reveal valuable information about changes of depth profiles of microstructure during sintering, e.g. a sintering induced diffusion of defects from sample interior to its surface.