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.

In recent years, advances in deep optical, and especially deep near-infrared imaging with the Hubble Space Telescope (HST) and wide-field ground-based telescopes such as VISTA, have revolutionized our understanding of the cosmological evolution of galaxies and supermassive black-holes (as manifest through active galactic nuclei; AGN). In particular, the dynamic range provided by the survey `wedding cake' of available HST+ground-based optical/IR data offers new opportunities to push the meaningful statistical study of galaxy and AGN evolution out to high redshifts. Much recent attention has focused, unsurprisingly, on using these new data to push studies of galaxy formation back to within a billion years of the Big Bang, and exploring the role of young galaxies in driving cosmic hydrogen reionization during the crucial era corresponding to redshifts z ≃ 6-10. However, these data have not been as thoroughly exploited at intermediate redshifts, and have only recently been used to explore black-hole/AGN evolution. In this thesis I utilise the latest deep optical/near-infrared imaging and spectroscopy to explore three key facets of cosmological evolution. First, I present a new, robust measurement of the evolving rest-frame ultraviolet (UV) galaxy luminosity function (LF) over the key redshift range from z ≃ 2 to z ≃ 4. My results are based on the high dynamic range provided by combining the Hubble Ultra Deep Field (HUDF), CANDELS/GOODS-South, and UltraVISTA/COSMOS surveys. I utilise the unparalleled multi-frequency photometry available in this survey `wedding cake' to compile complete galaxy samples at z ≃ 2; 3; 4 via photometric redshifts (calibrated against the latest spectroscopy). This study is important as the peak of star-formation is shown to happen within a redshift range z = 2 - 4 and determining the exact epoch that the galaxies were forming most of their stars depends significantly on the UV luminosity density which requires robust measurements of the galaxy UV luminosity function and its accurate parameterization. My new determinations of the UV LF extend from M1500 ≃ -22 (AB mag) down to M1500 =-14.5, -15.5 and -16 at z ≃2, 3 and 4 respectively (thus reaching ≃ 3-4 magnitudes fainter than previous blank-field studies at z ≃ 2 - 3). At z ≃ 2 - 3 I find a much shallower faint-end slope (α = -1:32 ± 0:03) than the steeper values (α ≃ -1:7) reported in the literature, and show that this new measurement is robust. By z ≃ 4 the faint-end slope has steepened slightly, to α = -1:43 ± 0:04, and I show that these measurements are consistent with the overall evolutionary trend from z = 0 to z = 8. I then calculate the UV luminosity density (and hence unobscured star-formation density) and show that it peaks at z ≃ 2:5 - 3, when the Universe was ≃ 2:5 Gyr old. Second, I have used these data to revisit the possibility that X-ray AGN played a significant role in cosmic hydrogen reionization which is one of the major processes in the formation of the Universe we see today. Hence, it is really important to understand this phenomenon thoroughly by studying the properties of sources capable of ionising photons, such as star-forming galaxies and high redshift AGNs. Although most recent studies have suggested that the emerging population of young star-forming galaxies can bathe the Universe in sufficient high-energy photons to complete reionization by z ≃ 6, some authors have reasserted the potentially important role of high-redshift AGN in the hydrogen reionization process. In an effort to clarify this situation, I reinvestigate a claimed sample of 22 X-ray detected active galactic nuclei (AGN) at redshifts z > 4, which has reignited the debate as to whether young galaxies or AGN reionized the Universe. These sources lie within the GOODS-S/CANDELS field, and I examine both the robustness of the claimed X-ray detections (within the Chandra 4Ms imaging) and perform an independent analysis of the photometric redshifts of the optical/infrared counterparts. I confirm the reality of only 15 of the 22 reported X-ray detections, and moreover find that only 12 of the 22 optical/infrared counterpart galaxies actually lie robustly at z > 4. I recalculate the evolving far-UV (1500Å) luminosity density produced by AGN at high redshift, and find that it declines rapidly from z ≃ 4 to z ≃ 6, in agreement with several other recent studies of the evolving AGN luminosity function. The associated rapid decline in inferred hydrogen-ionizing emissivity contributed by AGN falls an order-of-magnitude short of the level required to maintain hydrogen ionization at z ≃ 6. I conclude that AGNs make a very minor contribution to cosmic hydrogen reionization. Finally, I have utilized the deep optical/near-infrared survey data to explore the prevalence of quenched/passive galaxies at high redshift. Applying a robust method to isolate passive galaxies from star-forming galaxies is the key to improving our understanding of the quenching process. Focusing primarily on the deep HUDF data-set, I have revisited the effectiveness of simple colour-colour (UVJ) selection techniques in isolating robust samples of quenched galaxies, and find that dust plays a more important role in this selection process than has been previously appreciated. Through careful SED fitting I successfully isolate a sample of apparently dust-free quiescent galaxies in the redshift range 0:5 < z < 4:5 but (at least in the HUDF) fail to find any galaxy which has remained truly quiescent for > 1 Gyr. I conclude by focusing on the properties of a refined/robust sample of apparently quenched galaxies at z > 3, and in particular establishing the contribution of quenched galaxies to stellar-mass density at early times. I conclude with a summary of my findings, and a brief discussion of the most promising avenues for future advances with the next generation of facilities, such as the James Webb Space Telescope (JWST).