When a bubble oscillates in an acoustically driven pressure field, its oscillations result in an attractive force on micro-sized objects in the near field. At the same time, the objects are subject to a viscous drag force due to the streaming flow that is generated by the oscillating bubble. Based on these secondary effects, oscillating bubbles have recently been implemented in biological applications to control and manipulate micron-sized objects. These objects include live microorganisms, such as Caenorhabditis elegans and Daphnia (water flea), as well as cells and vesicles. Oscillating bubbles are also used in delivering drugs or genes inside human blood vessels. In this review paper, we explain the underlying physical mechanism behind oscillating bubbles and discuss some of their key applications in biology, with the focus on the manipulation of microorganisms and cells.