behaviour in seismological data. It focuses mainly on vertical arrays as an exceptional natural laboratory to study the propagation of seismic waves through the subsurface soil layers. The review highlights the breakthroughs that were performed such as the demonstration of the significance of the non-linear soil behaviour or the proposal of methodologies to back calculate the non-linear soil properties. The PGA is one of the most used parameters to describe the level of seismic solicitations. The reported PGA threshold from which non-linear soil behaviour is observed, has been decreasing since the 80’s thanks to the increase of available data, the improvement of the data quality, of the computational efficiency. The results of all studies lead to (1) new methodologies to invert data and provide in-situ characterisation of soil behaviour and (2) the definition of proxy parameters that reflect the impact of non-linear soil behaviour on site responses. From these proxies it is now possible to take into account non-linear soil behaviour in the analysis of site responses without using numerical simulations. Future perspectives in this field concern the densification of the instrumented sites and the characterisation of soil properties to provide natural laboratories that are well-constrained. For the assessment of the insitu non-linear soil properties, the quantification of the uncertainties and spatial variability also represent a challenge. To do so we need to gather even more the data which have been made available through international collaborations.