In this thesis, I explore multiple constraints on the properties of early galaxies, the reionization history, and the global 21 cm signal. Specifically, I use upper limits on the 21 cm power spectrum measured by the HERA interferometer, current and future measurements of the global 21 cm signal, and forecasts for high redshift Fast Radio Bursts (FRBs). Firstly, I examine the influence of cosmic reionization on FRBs. They are recently discovered extra-galactic sources of strong radio signals, and the dispersion measure of these signals is sensitive to the ionization state of the intergalactic medium. This analysis has previously only been done for specific reionization models; I propose using a model-independent parameterization of reionization. I employ synthetic data of future FRB measurements at high redshifts z>5 to show that (i) the model-independent method removes a significant bias in the inferred optical depth, and (ii) that the observation of high-z FRBs can facilitate direct and model-independent measurements of the reionization history and associated cosmological parameters. Secondly, I use Bayesian methods for a model-independent parameterization of the sky-averaged 21 cm signal. One of the biggest challenges in that field is identifying the cosmological signal among other systematic contributions and foregrounds. In my work, I compare two model-independent methods to fit the 21 cm signal and to separate out the foregrounds: (i) a Gaussian Process modelling the foreground-orthogonal component of the data, and (ii) a spline-based FlexKnot interpolation utilising Bayesian evidence to find the simplest signal (agnostic of its cosmological or systematic nature) that fits the data. I apply these methods to both, a synthetic validation data set and the EDGES observations. I find that both methods fully recover the foreground-orthogonal component of the signal and that the FlexKnot method is able to separate the signal from the foreground in the synthetic data. Using this novel analysis I discover a set of four different shapes that can explain the EDGES observations, only one of which resembles the originally reported absorption signal. Finally, I derive constraints on the astrophysical properties of early galaxies using 21 cm power spectrum observations from the HERA telescope. I derive a likelihood function to compare the data with cosmological models, develop a neural network emulator to speed up the computation of those cosmological models and analyze the measurements of two HERA data releases. I derive constraints on astrophysical parameters based on semi-numerical models, in particular focusing on models with non-standard radio backgrounds. The main constraint I find is that early galaxies cannot simultaneously produce low X-ray and high radio emissions, as such scenarios would produce a signal larger than the upper limits set by HERA.