I present an observational review of the five currently known accretion-driven millisecond X-ray pulsars. A prominent place in this review is given to SAX J1808.4-3658; it was the first such system discovered and currently four outbursts have been observed from this source. This makes SAX J1808.4-3658 the best studied example of the group. Its most recent outburst in October 2002 is of particular interest because of the discovery of two simultaneous kilohertz quasi-periodic oscillations and nearly coherent oscillations during type-I X-ray bursts. This is the first time that such phenomena are observed in a system for which the neutron star spin frequency is exactly known. The other four systems were discovered within the last two years and only limited results have been published. Since new exiting results are to be expected in the future for all five sources, this review will only represent a snap-shot of the current observational knowledge of accretion-driven millisecond X-ray pulsars. A more extended and fully up-to-date review can be found at http://zon.wins.uva.nl/~rudy/admxp/.