Intensity mapping with future radio-telescopes like the Square Kilometre Array (SKA) is expected to revolutionize cosmology. Those radio-telescopes will detect the redshifted 21cm emission from neutral hydrogen with an unprecedented precision. In order to extract the maximum information from those surveys an exquisite understanding of the distribution of neutral hydrogen is needed from the theoretical side. I will describe two different approaches to model the spatial distribution of neutral hydrogen in the post-reionization era, that reproduce the statistical properties of the DLAs at redshifts z~2-4. I will also discuss the range of scales where SKA will detect the 21cm power spectrum and the perspectives of imaging the neutral hydrogen distribution. Finally, I will discuss the cross-correlation of Lyman break galaxies and the 21cm signal and its usefulness to avoid foregrounds contamination.