Acoustofluidics, which combines ultrasonic waves with fluidics, offers several unique features enabling non-contact, label-free, bio-compatible, and precise manipulation of micro-objects. Surface acoustic wave (SAW) is a type of ultrasonic wave that propagates on a substrate's surface and is limited to a thickness ~µm at the surface. When coupled with microfluidic systems, SAW renders exceptional control over the manipulation of micro-objects. The present dissertation focuses on exploring the capabilities of SAW to manipulate micro-objects such as rigid particles, blood cells, and droplets in confined geometries and on open surfaces. Manipulations in confined geometries comprise studying the behavior of microparticle aggregation in dense suspensions and coalescence of droplets in circular microwell structures under the action of SAW. The physics governing the particle aggregation behavior in a dense suspension under SAW microcentrifugation is elucidated, and the separation of plasma from human blood samples is demonstrated. Subsequently, the phenomenon of coalescence of a pair of droplets in a circular microwell under SAW is investigated, and the possibility for multi-droplet coalescence is illustrated. Further, the wetting behavior of a sessile droplet on a nanostructured superhydrophobic surface under SAW actuation is studied, which led to the observation of on-demand Cassie-Wenzel wetting transition induced by SAW.