Surface Acoustic Wave (SAW) filters have been extensively developed for more than 50 years for mobile communication systems. During that time, several innovations have been transforming the corresponding engineering domain, on both design and manufacturing aspects. One major change in that dynamics consisted in modifying the substrate nature, from single crystal piezoelectric crystals to composite layered substrates based on oriented single crystal submicron layers. Lithium Niobate and Tantalate were particularly considered for this development because of their capability to address bandwidths in the 0.1-10% range with insertion losses better than 2 dB. Pioneer work conducted in early 2000 has been matured and gave rise to a first demonstration of filter with breakthrough performances less than 10 years ago. However, the SAW industry community rapidly adopted that approach, definitely changing the mindset and practices of SAW filter designers to answer the increasing demands from new generations of telecommunication standards. Among the main changes offered by these new substrates, temperature stability, loss reduction, coupling enhancement and power handling are the most attractive features pushing designers to definitely adopt the new approach. In this presentation, we review the main physical principles of SAW excited on the so-called Piezo-On-Insulator (POI) wafers. The remarkable characteristics of acoustic propagation on such wave-guides are presented and discussed, particularly to emphasize their impact on filter operation and quality. Similarly to any inhomogeneous waveguide, waves propagating on POI exhibit dispersive properties, requiring accurate theoretical tools to properly control the associated physical properties. Figure-Of-Merits qualifying the corresponding operation are detailed and state-of-the-art figures are provided for the different frequency ranges addressable with this solution. Filters based on SAW on POI are presented to illustrate their benefits for various frequency range and filter characteristics such as bandwidth, insertion losses and rejection. In particular, SAW-on-POI allows for alternate filter structures, taking advantage of the original wave properties on such substrates and therefore the different filter architectures are associated with specific demands to answer RF signal processing specification at best. To conclude, we show SAW-on-POI perspectives in all classical SAW domains, including a benchmark with BAW filters in S and C band