This paper reviews recent progress on microwave clocks using laser cooled neutral atoms. With an ultra-stable cryogenic sapphire oscillator as interrogation oscillator, a cesium fountain operates at the quantum projection noise limit. With 6.10(5) detected atoms, the relative frequency stability delta nu/nu is 4(.)10(-14)tau (-1/2) where tau is the integration time in seconds. This stability is comparable to that of hydrogen masers. At tau = 2(.)10(4)s, the measured stability reaches 6(.)10(-16). Equally important is the accuracy of the frequency standard since Cs-133 is the primary reference for the definition of the time unit, the second. The accuracy of our cesium fountain FO1 is presently 1.10(-15), currently the best reported value.A Rb-87 fountain has also been constructed and the Rb-87 ground-state hyperfine energy has been compared to the Cs primary standard with a relative accuracy of 2(.)5(.)10(-15). Comparing the hyperfine energies of atoms with different atomic numbers Z, one can search for possible variations of the fine structure constant alpha = e(2)/hc with time. Measurements of the ratio nu(Rb-87)/nu(Cs-133) spread over an interval of 24 months indicate no change at a level of 3.110(-15)/year, placing a new upper limit for 1/alpha (d alpha /dt). The second attractive feature of Rb-87 fountains is the smallness of the frequency shift induced by the mean field interaction between atoms. This shift is found to be at least similar to 50 times below that of cesium.Finally, the interest of the microgravity of space for cold atom experiments is outlined. A space mission, ACES, carrying ultra-stable clocks, is presented. ACES has been selected by the European Space Agency to fly on the International Space Station in 2004.