Optical trapping using focused laser beams (laser tweezers) has been proven to be extremely useful for contactless manipulation of a variety of small objects, including biological cells, organelles within cells, and a wide range of other dielectric micro- and nano-objects. Colloidal metal nanoparticles have drawn increasing attention in the field of optical trapping because of their unique interactions with electromagnetic radiation, caused by surface plasmon resonance effects, enabling a large number of nano-optical applications of high current interest. Here we try to give a comprehensive overview of the field of laser trapping and manipulation of metal nanoparticles based on results reported in the recent literature. We also discuss and describe the fundamentals of optical forces in the context of plasmonic nanoparticles, including effects of polarization, optical angular momentum, and laser heating effects, as well as the various techniques that have been used to trap and manipulate metal nanoparticles. We conclude by suggesting possible directions for future research.