  This paper describes advances in microwave frequency standards using
laser-cooled atoms at BNM-SYRTE. First, recent improvements of the $^{133}$Cs
and $^{87}$Rb 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 $1.6\times 10^{-14}\tau^{-1/2}$ where $\tau $
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 $2\times 10^{-16}$ at $50,000s
for the first time for primary standards. In addition, these clocks realize the
SI second with an accuracy of $7\times 10^{-16}$, one order of magnitude below
that of uncooled devices. In a second part, we describe tests of possible
variations of fundamental constants using $^{87}$Rb and $^{133}$Cs 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.
