We review the state of the art of the study of the cosmic structure on ultra-large scales as is forecast to be achievable by the oncoming generation of intensity mapping experiments. We focus on intensity maps of the redshifted 21 cm line radiation of neutral hydrogen (Hi) in the post-reionisation Universe. Such measurements will be performed by future radio telescopes such as for instance the Square Kilometre Array and will allow for surveying the biggest volume ever of cosmic structure. After having shown why it is valuable to scrutinise such extremely large cosmic scales-they will supply crucial information about the physical processes at play at early times-we concentrate on primordial non- Gaussianity as a working example. We illustrate that Hi intensity mapping experiments can place tight bounds on different inflationary scenarios via constraining the non-Gaussianity parameter, fNL, with an error close to 1.