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.