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, 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.In the context of 21cm radiation, this study identifies two approaches which will increase the information gain from future observations, a numerical and an analytic approach.The numerical challenges of future analyses are a consequence of the data rates of next generation telescopes, and is addressed by introducing machine learning techniques as a possible solution. Artificial neural networks have gained much attention in both the scientific and commercial world, and we use these as a way to emulate numerical simulations. Further, this project identifies the potential of high order statistical measurements as a cosmological probe in the context of late-time 21cm experiments. This is shown to constrain cosmological parameters beyond the capabilities of CMB observations.