Liquid crystals have been all along a fertile background for scientific research, from mathematics to material science and optics; their use is not limited to displays but extends to nonlinear optics, for instance, to switching and routing of optical beams. Due to their extreme sensitivity to electric fields, and this at frequencies ranging from continuous to optical ones, they are also nonlinear media supporting the generation and propagation of self confined beams, called spatial optical solitons, at very low powers. Spatial optical solitons have the property to propagate without diffraction, since this is compensated by nonlinear self-focusing in the medium, resulting in self-induced waveguides. In nematic liquid crystals, these waveguides can in turn confine and route other optical signals and can be reconfigured, either optically or electrically, as soliton trajectories can be controlled by other fields, paving the way to all-optical manipulation. Nematic liquid crystals have also been recently employed with success in the so-called singular optics, in which the key parameter is the topologic singularity carried by the phase of an electromagnetic wave. In this thesis I will report on my work on spatial optical solitons and optical singularities in nematic liquid crystals.
