The fabrication of GaAs-GaAIAs coupled quantum dots and of quantum rings using electron beam lithography and dry etching is described. Coupled dots of physical diameter of 500 and 250 nm were fabricated and processed with top electrical contacts to apply an electric field. We show that the emission spectrum of coupled dots is modified by the electric field. Quantum rings of 400 nm outer diameter and wall thickness of 25 nm were fabricated. The emission spectrum from rings showed the quantum well emission shifted to higher energies and although its intensity decreased by about one order of magnitude there was little linewidth broadening.