This thesis considers various topics and open questions in galaxy formation during the epoch of reionization and presents multiple new computational techniques developed specifically to study this era. This work naturally divides into two main sections: 1) The formation of the first massive black holes and 2) Interpreting ALMA observations of galaxy formation during the epoch of reionization. The first topic addresses the existence of super massive black holes (SMBHs) with $MBH>109$M$\mathrm{<mrow\; data-mjx-texclass="ORD">\odot </mrow>}$ at $z>6$. It is well established that stellar mass black holes are very unlikely to be able to accrete matter efficiently enough to grow to this mass at this redshift. For this reason, many alternative channels have been proposed for black hole formation that produce objects with significantly larger initial masses. In this thesis, I consider a mechanism whereby runaway stellar collisions in dense primordial star clusters form a very massive star that is likely to collapse to an intermediate mass black hole (IMBH) with $MBH>103$M$\mathrm{<mrow\; data-mjx-texclass="ORD">\odot </mrow>}$. In order to test this scenario, I added 12 species non-equilibrium chemistry to the massively parallel adaptive mesh refinement code RAMSES, and simulated, at sub-pc resolution, the collapse of the first metal-enriched halo which is likely to host a Population II star cluster. The properties of the central gas cloud in the collapsing halo were then extracted from the simulation and used to create initial conditions for the direct N-body integrator, NBODY6. These star clusters were simulated for 3.5Myr (until the first supernova is expected to occur) and it was determined that the properties of the gas clouds that form in cosmological simulations were indeed suitable to form a very massive star by collisional runaway. This suggests that this mechanism is a promising channel for forming the seeds of SMBHs at high redshift. The second topic of this thesis aims to help interpret the plethora of recent and upcoming ALMA observations of star forming galaxies during the epoch of reionization. These observations target far-infrared lines such as [CII] and [OIII] which directly probe the interstellar medium (ISM) of these $z>6$ galaxies. In order to study this epoch, I employ the RAMSES-RT code, which allows for the computation of multifrequency radiative transfer on-the-fly. I modified this code in a number of ways so that it can handle radiation-coupled H$2$ non-equilibrium chemistry (including Lyman-Werner band radiation) and I developed the variable speed of light approximation which changes the speed of light in the simulation depending on the density of gas so that ionisation fronts propagate at the correct speed in all gas phases. Cosmological boxes were initialised to include galaxies with masses comparable to the observations of Maiolino et al. (2015) and run at various resolutions to test convergence properties. One of the major goals of this study was to identify the physical mechanism responsible for the spatial offset observed between [CII] and UV/Lyα in many high-redshift galaxies. (Abridged)