The field of levitation optomechanics---or levitodynamics---studies the manipulation and control of small trapped objects in an isolated environment, providing a gateway to answer fundamental questions in physics and expanding the range of applications at the nanoscale. Levitation of particles can be achieved through different tools and techniques such as Paul traps and optical tweezers. Paul traps are created by alternating electric fields to levitate charged particles, while optical traps are based on optical forces that confine and manipulate nano-objects with high polarizability and low absorption. Both have the potential to be reduced to on-a-chip systems, enabling the miniaturization of the experiment, its interface with other p...