Acoustic fields are ideal for micromanipulation, being biocompatible and with force gradients approaching the scale of single cells. They have accordingly found use in a variety of microfluidic devices, including for microscale patterning, separation, and mixing. The bulk of work in acoustofluidics has been predicated on the formation of standing waves that form periodic nodal positions along which suspended particles and cells are aligned. An evolving range of applications, however, requires more targeted micromanipulation to create unique patterns and effects. To this end, recent work has made important advances in improving the flexibility with which acoustic fields can be applied, impressively demonstrating generating arbitrary arrangements of pressure fields, spatially localizing acoustic fields and selectively translating individual particles in ways that are not achievable via traditional approaches. In this critical review we categorize and examine these advances, each of which open the door to a wide range of applications in which single-cell fidelity and flexible micromanipulation are advantageous, including for tissue engineering, diagnostic devices, high-throughput sorting and microfabrication.