I will discuss new methods of the dark matter (DM) direct detection with the use of atomic clocks on ground and in space. The dark matter is assumed to exist in a form of waves of ultra-light scalar fields or in a form of topological defects (monopoles, strings and domain walls). Presence of DM may lead to the local change of fundamental constants affecting the atomic clock transition frequencies. Such
change will create characteristic anomalies in the clock stability diagrams. We used existing data on the Al+/Hg+ optical clock comparison to put the first limits on the dilaton dark matter in the region of masses m > 1E-15 eV. We also estimate the sensitivities of future atomic clock experiments in space, in particular, the caesium and strontium clocks aboard the International Space Station, as well as a potential thorium nuclear clock. These experiments are expected to put first limits on the topological dark matter in the range of masses 1E-10 eV < m < 1E-6 eV. If the time permits, I will also comment on the vector DM detection methods with atom interferometers.