With the continuing development of high-sensitivity radio antennas, cosmological probes of matter-density perturbation will have a new opportunity in the radio band frequency, adding a redundancy to current and future cosmological probes. The 21-cm-wavelength line from neutral hydrogen atoms will enable us to map 3D distribution of matter in the universe. We review the current status of observational endeavors in terms of the diffuse intensity mapping and the galaxy survey, together with recent theoretical developments which would impact the observation. We show that non-standard cosmological models other than LCDM will have the best chance to be observed with the high-redshift 21-cm cosmology.