Advanced fully site-specific seismic hazard assessment methods need two main elements. They need first an accurate estimation of the local amplification. Then, they need a reliable reference ground motion at the base of the soil column. In order to make progress toward site-specific applications in low-to-moderate seismicity context, the CASHIMA (Cadarache seismic hazard integrated multidisciplinary assessment) program coordinated numerous research actions since 2005. This paper is a synthesis of the achieved works. As for the local amplification estimation, we conclude that both simulations and empirical measurements are mandatory empirical measurements are required to calibrate the simulations. Conversely, simulations are mandatory to extrapolate the amplification estimates beyond the seismic scenarios previously recorded by instrumentation. The definition of the hard-rock ground motion is a critical part of the fully site-specific seismic hazard study. Indeed, the current Ground Motion Prediction Equations (GMPEs) are poorly constrained for hard-rock sites. The standard procedure is to adjust the GMPEs from the host to the target site conditions by applying so-called V$_S$-$\kappa$ adjustments. In such approach, the most critical parameter is the "target" site $\kappa_0$. In low-seismicity areas, the collection of a sufficient number of records is difficult. Moreover, the $\kappa_0$ physical bases are not fully understood. An alternative approach, that does not use $\kappa_0$ and that involves a correction of the local amplification at each accelerometric site, was developed on a subset of the Kik-net database. The results showed significant differences with respect to the standard host-to-target approaches. In conclusion, as soon as these new GMPEs will be developed to allow the definition of consistent hard-rock ground motion, including datasets specific to European context, we estimate that fully site-specific seismic hazard study can be applied in low-to-moderate seismicity area.