We demonstrate that surface acoustic waves (SAWs), nanometer amplitude Rayleigh waves driven at megahertz order frequencies propagating on the surface of a piezoelectric substrate, offer a powerful method for driving a host of extremely fast microfluidic actuation and micro/ bioparticle manipulation schemes. We show that sessile drops can be translated rapidly on planar substrates or fluid can be pumped through microchannels at 1-10 cm/s velocities, which are typically one to two orders quicker than that afforded by current microfluidic technologies. Through symmetry-breaking, azimuthal recirculation can be induced within the drop to drive strong inertial microcentrifugation for micromixing and particle concentration or separation. Similar micromixing strategies can be induced in the same microchannel in which fluid is pumped with the SAW by merely changing the SAW frequency to rapidly switch the uniform through-flow into a chaotic oscillatory flow by exploiting superpositioning of the irradiated sound waves from the sidewalls of the microchannel. If the flow is sufficiently quiescent, the nodes of the transverse standing wave that arises across the microchannel also allow for particle aggregation, and hence, sorting on nodal lines