Laser trapping of particles in three dimensions can occur as a result of the refraction of strongly focused light through micrometre-sized particles. The use of this effect to produce laser tweezers is extremely common in fields such as biology, but it is only relatively recently that the technique has been applied to liquid crystals (LCs). The possibilities are exciting: droplets of LCs can be trapped, moved and rotated in an isotropic fluid medium, or both particles and defects can be trapped and manipulated within a liquid crystalline medium. This paper considers both the possibilities. The mechanism of transfer of optical angular momentum from circularly polarized light to small droplets of nematic LCs is described. Further, it is shown that droplets of chiral LCs can be made to rotate when illuminated with linearly polarized light and possible mechanisms are discussed. The trapping and manipulation of micrometre-sized particles in an aligned LC medium is used to provide a measure of local shear viscosity coefficients and a unique test of theory at low Ericksen number in LCs.