Floor acoustic waves (SAWs)-matter interplay gives an interesting doorknob for inducing and manipulating novel phenomena and functionalities in two-dimensional (2D) supplies. The dynamic pressure discipline and piezo-electric discipline related to propagating SAWs decide the coherent manipulation and transduction between 2D excitons and phonons. Over the previous decade, many intriguing acoustic-induced results together with acousto-electric impact, acousto-galvanic impact, acoustic Stark impact, acoustic Corridor impact and acoustic exciton transport, have been reported experimentally. However many extra phenomena, resembling valley acousto-electric impact, valley acousto-electric Corridor impact and acoustic spin Corridor impact, was theoretically proposed, ready for experimental verification. On this minireview, we try to overview the latest breakthrough of SAWs-induced phenomena protecting acoustic cost transport, exciton transport and modulation and coherent acoustic phonons. Views on the alternatives of proposed SAWs-induced phenomena, in addition to open experimental challenges, are additionally mentioned trying to supply some guideline for experimentalists and theorists to discover desired unique properties and enhance sensible purposes of 2D supplies.