The time in the history of the Universe when the first stars and galaxies formed and ionized the gas in the intergalactic medium is known as the Epoch of Reionization. This transformative time period, which took place within the first billion years after the Big Bang, is still relatively unexplored due to the significant difficulties associated with observing so far back in time. The theme of this thesis is tying together existing (mostly indirect) and upcoming observations with simulations. Papers I and II deal with Lyα emitting galaxies. The Lyα emission line is very sensitive to neutral hydrogen, which was plentiful during the Epoch of Reionization. Therefore, observations of distant Lyα galaxies may be used to indirectly tell us something about when and how reionization took place. Properly interpreting the observations is, however, far from straightforward. In Paper I we develop a new method for combining large, low-resolution simulations of the intergalactic medium with small, high-resolution simulations of individual galaxies. We use this method to reproduce existing observations. In Paper II we use the same method to make predictions for future observations. Another observational probe of the EoR is the 21-cm emission line from neutral hydrogen. This line is the most promising probe for directly studying the neutral gas in the early Universe, and several radio telescopes are currently gathering data to observe it. The 21-cm signal is affected by a multitude of cosmological and astrophysical effects, all of which need to be understood in order to interpret the upcoming observations. One such effect is the non-random shifts in redshifts caused by the peculiar velocity of matter flowing towards higher-density regions. This effect, known as redshift space distortions, is the topic of papers III and IV, while paper V deals with another observational effect called the lightcone effect.