With the Hubble Space Telescope and its near-infrared capabilities, it is now possible to probe deep into the epoch of reionization, improving our understanding of galaxy evolution through cosmic history. Whether it is via colour-selection or fitting the spectral energy distribution, it has now become routine to amass large samples of galaxies as distant as redshift z = 8, with the current frontier of observations at z = 9 - 10. The new Hubble Frontier Fields (HFF) programme provides the potential to study the most distant, intrinsically faint background galaxies through the gravitational lensing provided by a foreground galaxy cluster. This thesis presents a study of the galaxy population at z = 9 - 10 that exploits this phenomenon. In an initial search of the first two HFF cluster+parallel pointings, Abell 2744 and MACS J0416.1-240, we unveil twelve candidate high-redshift galaxies at 8:4 < z < 9:5, and are thus able to place constraints on the galaxy UV luminosity function at z = 9. For this study, we employ the "blank-field" method, whereby we confine attention to only the homogeneously deep, relatively low-magnification regions of the imaging. We are able to demonstrate evidence for a smooth decline in UV luminosity density between z ≃ 8 and z ≃ 9, in contrast to reports in the recent literature of a steep drop-off at these redshifts. We extend this study to include the new MACS J0717.5+3745 and MACS J1149+2223 cluster+parallel pointings, and supplement the search for z ≃ 9-10 galaxies with twenty CLASH cluster pointings. From a search over an area ≃ 130 sq. arcmin, we are able to present 33 galaxy candidates with photometric redshift solutions in the range 8:4 < zphot < 11:2. Our new results reinforce the argument for a smoothly-evolving LF between z ≃ 8 and z ≃ 9, which can be equally well modelled by a factor ≃ 2 drop in ϕ* or a dimming of ≃ 0:5 mag in M*. We also find evidence that this smooth decline in the UV luminosity function, and hence UV luminosity density, continues to z ≃ 10. As well as considering the galaxy population at z = 9 - 10, this thesis presents a study of the stellar populations of galaxies at z ≥ 5. We are able to extend the luminosity baseline and measure the colour-magnitude relation at z = 5 - 8, through a combination of probing intrinsically faint galaxies behind cluster fields, in conjunction with both ultra-deep, pencil beam imaging such as the Hubble Ultra Deep Field (HUDF) and wider, shallower imaging from the Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey (CANDELS). This allows us to make inferences about the underlying stellar populations of galaxies at these epochs, and provides a unique insight into the colours of intrinsically faint, lensed galaxies as faint as M1500 ~ -14. We find that the data is consistent with an essentially unchanged average UV slope (β) for a given luminosity across the redshift range z = 5-8. We also find that the data favours a mild flattening of the colour-magnitude relation with redshift between z = 5 and z = 8.