Optical nanoparticles are nowadays one of the key elements of photonics. They do not only allow optical imaging of a plethora of systems (from cells to microelectronics), but, in many cases, they also behave as highly sensitive remote sensors. In recent years, it has been demonstrated the success of optical tweezers in isolating and manipulating individual optical nanoparticles. This has opened the door to high resolution single particle scanning and sensing. In this quickly growing field, it is now necessary to sum up what has been achieved so far to identify the appropriate system and experimental set-up required for each application. In this review article we summarize the most relevant results in the field of optical trapping of individual optical nanoparticles. After systematic bibliographic research, we identify the main families of optical nanoparticles in which optical trapping has been demonstrated. For each case, the main advances and applications have been described. Finally, we also include our critical opinion about the future of the field, identifying the challenges that we are facing.