Optomechanics is concerned with the use of light to control mechanical objects. As a field, it has been hugely successful in the production of precise and novel sensors, the development of low-dissipation nanomechanical devices, and the manipulation of quantum signals. Micro-and nano-particles levitated in optical fields act as nanoscale oscillators, making them excellent lowdissipation optomechanical objects, with minimal thermal contact to the environment when operating in vacuum. Levitated optomechanics is seen as the most promising route for studying high-mass quantum physics, with the promise of creating macroscopically separated superposition states at masses of 10 6 amu and above. Optical feedback, both using active monitoring or the passive interaction with an optical cavity, can be used to cool the centre-of-mass of levitated nanoparticles well below 1 mK, paving the way to operation in the quantum regime. In addition, trapped mesoscopic particles are the paradigmatic system for studying nanoscale stochastic processes, and have already demonstrated their utility in state-of-the-art force sensing. * Electronic address: james.millen@kcl.ac.uk arXiv:1907.08198v1 [physics.optics] 18 Jul 2019It is a pleasant coincidence, that whilst writing this review the Nobel Prize in Physics 2018 was jointly awarded to the American scientist Arthur Ashkin, for his development of optical tweezers. By focusing a beam of light, small objects can be manipulated through radiation pressure and/or gradient forces. This technology is now available offthe-shelf due to its applicability in the bio-and medical-sciences, where it has found utility in studying cells and other microscopic entities.The pleasant coincidences continue, when one notes that the 2017 Nobel Prize in Physics was awarded to Weiss, Thorne and Barish for their work on the LIGO gravitational wave detector. This amazingly precise experiment is, ultimately, an optomechanical device, where the position of a mechanical oscillator is monitored via its coupling to an optical cavity. The field of optomechanics is in the ascendency [1], showing great promise in the development of quantum technologies and force sensing. These applications are somewhat limited by unavoidable energy dissipation and thermal loading at the nanoscale [2], which despite impressive progress in soft-clamping technology [3] means that these technologies will likely always operate in cryogenic environments.Enter the work of Ashkin: he showed that dielectric particles could be levitated and cooled under vacuum conditions in 1977 [4]. By levitating particles at low pressures, they naturally decouple from the thermal environment, and since the mechanical mode is the centre-of-mass motion of a particle, energy dissipation via strain vanishes. The field of levitated optomechanics really took off in 2010, when three independent proposals illustrated that levitated nanoparticles could be coupled to optical cavities [5][6][7]. This promises cooling to the quantum regime, and state engineering once you are t...