Surface acoustic waves (SAWs)-matter interaction provides a fascinating doorknob for inducing and manipulating novel phenomena and functionalities in two-dimensional (2D) materials. The dynamic strain field and piezo-electric field associated with propagating SAWs determine the coherent manipulation and transduction between 2D excitons and phonons. Over the past decade, many intriguing acoustic-induced effects including acousto-electric effect, acousto-galvanic effect, acoustic Stark effect, acoustic Hall effect and acoustic exciton transport, have been reported experimentally. But many more phenomena, such as valley acousto-electric effect, valley acousto-electric Hall effect and acoustic spin Hall effect, was theoretically proposed, waiting for experimental verification. In this minireview, we attempt to overview the recent breakthrough of SAWs-induced phenomena covering acoustic charge transport, exciton transport and modulation and coherent acoustic phonons. Perspectives on the opportunities of proposed SAWs-induced phenomena, as well as open experimental challenges, are also discussed attempting to offer some guideline for experimentalists and theorists to explore desired exotic properties and boost practical applications of 2D materials.