  We analyze possible effects of the dark matter environment on the atomic
clock stability measurements. The dark matter is assumed to exist in a form of
waves of ultralight scalar fields or in a form of topological defects
(monopoles and strings). We identify dark matter signal signatures in clock
Allan deviation plots that can be used to constrain the dark matter coupling to
the Standard Model fields. The existing data on the Al+/Hg+ clock comparison
are used to put new limits on the dilaton dark matter in the region of masses m
> 10^{-15} eV. We also estimate the sensitivities of future atomic clock
experiments in space, including the cesium microwave and strontium optical
clocks aboard the International Space Station, as well as a potential nuclear
clock. These experiments are expected to put new limits on the topological dark
matter in the range of masses 10^{-10} eV < m < 10^{-6} eV.
