Cosmology in the 21st century has matured into a precision science. Measurements of the cosmic microwave background, galaxy surveys, weak lensing studies and supernovae surveys all but confirm that we live in a geometrically flat Universe dominated by a dark energy component where most of the matter is dark. Yet, challenges to this model remain as well as periods in its evolution unobserved at present. The next decade will see the construction of a new generation of telescopes poised to answer some of these remaining questions and peer into unseen depths. Because of the technological advances of the previous decades and the scale of the new generation of telescopes, for the first time, cosmology will be constrained through the observation of the cosmic 21cm signal emitted by hydrogen atoms across the Universe. Being the ubiquitous element present throughout the different evolutionary stages of the Universe, neutral hydrogen holds great potential to answer many of the remaining challenges which face cosmology today. In the context of 21cm radiation, we identify two approaches which will increase the information gain from future observations, a numerical as well as an analytic approach. The numerical challenges of future analyses are a consequence of the data rates of next generation telescopes, and we address this here introducing machine learning techniques as a possible solution. Artificial neural networks have gained much attention in both the scientific and commercial world, and we apply one such network here as a way to emulate numerical simulations necessary for parameter inference from future data. Further, we identify the potential of the bispectrum, the Fourier transform of the three-point statistic, as a cosmological probe in the context of low redshift 21cm intensity mapping experiments. This higher order statistical analysis can constrain cosmological parameters beyond the capabilities of CMB observations and power spectrum analyses of the 21cm signal. Lastly, we focus on a fully 3D expansion of the 21cm power spectrum in the natural spherical basis for large angle observations, drawing on the success of the technique in weak lensing studies.