This paper describes advances in microwave frequency standards using laser-cooled atoms at BNM-SYRTE. First, recent improvements of the 133Cs and 87Rb atomic fountains are described. Thanks to the routine use of a cryogenic sapphire oscillator as an ultra-stable local frequency reference, a fountain frequency instability of 1.6 × 10−14 τ−1/2 where τ is the measurement time in seconds is measured. The second advance is a powerful method to control the frequency shift due to cold collisions. These two advances lead to a frequency stability of 2 × 10−16 at 50 000 s for the first time for primary standards. In addition, these clocks realize the SI second with an accuracy of 7 × 10−16, one order of magnitude below that of uncooled devices. In a second part, we describe tests of possible variations of fundamental constants using 87Rb and 133Cs fountains. Finally we give an update on the cold atom space clock PHARAO developed in collaboration with CNES. This clock is one of the main instruments of the ACES/ESA mission which is scheduled to fly on board the International Space Station in 2008, enabling a new generation of relativity tests.