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Summary form only given. Laser-cooled ions in radiofrequency traps are the atomic systems that allow the highest resolution (ratio of frequency to linewidth) in optical or microwave spectroscopy. They can serve as references in highly stable frequency standards and also enable precise tests of fundamental physics. We present recent results on our In/sup +/ optical frequency standard, based on the 5s/sup 2/ /sup 1/S/sub 0//spl rarr/5s5p /sup 3/P/sub 0/ transition at 236.5 nm wavelength. This transition has a natural linewidth of only 0.82 Hz and is highly immune to systematic frequency shifts.