We propose using the Josephson vortices (fluxons) as adjustable and malleable waveguides of electromagnetic radiation. Our theoretical and numerical calculations show that electromagnetic waves can propagate along the Josephson vortices and always follow the vortex lines. By changing external parameters, such as electric currents or magnetic fields, the shape and configuration of the guiding vortex lines can be controlled. We describe the design of a multifunctional three-terminal device that controls the transmission (redirecting or splitting) of a beam of electromagnetic waves.