In this paper experiments with single trapped ions are reviewed. They are performed with the aim of developing a new frequency standard and to perform cavity quantum electrodynamics experiments with single ions. For a new optical frequency standard we are investigating the 5s21S0 implied by 5s5p3P0 transition of a single trapped laser-cooled 115In(superscript + ion. This line with a natural linewidth of only 0.8 Hz is highly immune to systematic frequency shifts. For sideband laser cooling and fluorescence detection of the indium ion the 5s21S0 implied by 5s5p3P1 transition at 230.6 nm is used. Temperatures below 100 (mu) K and a mean vibrational quantum number <n><1 of the ion in the trap have been reached. For the clock transition a resolution of 1.3 multiplied by 10-13 (linewidth 170 Hz) has been obtained so far, limited by the short term frequency fluctuations of the clock laser. The absolute frequency of the 1S0 implied by 3P0 transition was measured by making a link to the reference frequency of the methane-stabilized HeNe laser using a frequency chain. In the second part of the paper the present status of the experiments on the ion trap laser are briefly described.