Advances in electro-optical technology have led to the production of designer optical beams. These are beams of light with unique shapes and properties. Their study leads to new forms of communication and analysis using light. A unique feature of these optical beams is that they can carry peculiar features, such as optical vortices, polarization singularities, and angular momentum. Our starting point will be to generate a type of beams that are self-healing (i.e., that they reconstruct past an obstacle), to further manipulate them, and investigate the new properties that they acquire.