Novel approaches, combining technology, biomaterial design, and cutting-edge cell culture, have been increasingly considered to advance the field of tissue engineering and regenerative medicine. Within this context, acoustic manipulation to remotely control spatial cellular organization within a carrier matrix has arisen as a particularly promising method during the last decade. Acoustic or sound-induced manipulation takes advantage of hydrodynamic forces exerted on systems of particles within a liquid medium by standing waves. Inorganic or organic particles, cells, or organoids assemble within the nodes of the standing wave, creating distinct patterns in response to the applied frequency and amplitude. Acoustic manipulation has advanced from micro- or nanoparticle arrangement in 2D to the assembly of multiple cell types or organoids into highly complex in vitro tissues. In this review, we discuss the past research achievements in the field of acoustic manipulation with particular emphasis on biomedical application. We survey microfluidic, open chamber, and high throughput devices for their applicability to arrange non-living and living units in buffer or hydrogels. We also investigate the challenges arising from different methods, and their prospects to gain a deeper understanding of in vitro tissue formation and application in the field of biomedical engineering.