Optical beams propagating in three-dimensional free space are complex scalar fields, and typically contain nodal lines (optical vortices) which may be thought of as generalized interference fringes and topological singularities of phase. Optical vortices were originally discovered by Hans Wolter in 1950 in his study of total internal reflection, and are now a major area of study of classical light fields, appearing ubiquitously in spatially varying wave functions. Random wave fields, representing optical speckle patterns scattered from rough surfaces, have a tangled skeleton of nodal lines, some of which are closed loops, and others are infinite, open lines. Computer simulations of random superpositions of plane waves indicate that these lines have the fractal properties of brownian random walks with characteristic scaling of the probability that pairs of loops are linked together. Holographically-controlled laser beams provide the opportunity to control the form of optical fields and the nodal lines within them. Using the theory of fibred knots, I will describe the design of superpositions of laser modes (effectively solutions of the 2+1 Schrödinger equation) which contain isolated knots and links. I will conclude by explaining how these mathematical fields have been experimentally realized by the experimental Optics group in Glasgow, UK.