The first chapter in this new volume analyzes the basic properties of optical vortices (OV) and different techniques for their investigation within a frame of linear optics of monochromatic light wave. Chapter two considers the experimental methods of OV creation and different techniques for their recognition. Chapter three concentrates on the forces and torques exerted on transparent and absorbing particles trapped in laser beams containing optical vortices. Previous theoretical and experimental work is reviewed and the new calculations of the effect of vortex beams on absorbing particles are presented. Chapter four examines the vortex core size and how it affects the propagation dynamics of neighboring optical vortices in the same beam. The last chapters discuss the dynamics of optical vortices when anisotropy of the nonlinear medium plays a decisive role. In these sections the theoretical framework describing nonlinear propagation in photorefractive media is described. The resulting set of coupled equations for the dynamics of the optical field, and the optically induced material potential, are used for the subsequent theoretical and numerical development in the following sections.