Neutral hydrogen (HI) is the most abundant baryonic element and a crucial component of galaxies. In the early universe, the interaction between neutral gas and the light produced by galaxies is thought to have given rise to cosmological reionization. During this last major phase transition of the Universe, the bulk of HI within the intergalactic medium (IGM) was ionized. However, observational constraints limit our understanding of the interplay between the radiation produced by galaxies and their neutral gas, and that of the physical processes that caused this important cosmological period. Another poorly understood mechanism is the one that drives the escape of Lyman-α (Lyα) emission from star-forming galaxies and shapes the line profile of this well-used tracer of galaxies at high redshift. To fully answer these questions, direct observations of the neutral gas content and distribution of Lyα emitters are needed.

This thesis presents 21cm observations of the neutral gas reservoirs of rare local galaxies that are analogous to objects in the early universe. We have observed the neutral gas of Haro 11, the closest known ionizing radiation (Lyman Continuum, LyC) leaking galaxy. This 21cm observation was the first to successfully map the neutral gas distribution of a confirmed LyC emitter. We observed a strongly asymmetric neutral gas distribution resulting from a merger event, with the bulk of the HI mass offset from the regions producing LyC radiation in the galaxy. By decreasing the column density of gas on large scales, this HI distribution has facilitated the escape of ionizing radiation from the center of the galaxy to the IGM.

We have also observed the neutral gas content and distribution of local Lyα-emitting galaxies on a variety of angular scales. We mapped the neutral gas at scales that can be compared to those characterizing Lyα emission in two galaxies, and supplemented the data with integral field spectroscopic observations tracing ionized gas and dust. Additionally, we reduced low angular resolution 21cm observations of 37 galaxies in the Lyman Alpha Reference Samples. We found clear evidence of interaction in most of the galaxies in the samples (~60%), indicating that mergers play an important role in the Lyα escape from galaxies. We found that global HI properties did not correlate well with any metric quantifying Lyα emission, although different classes of Lyα-emitters were distributed differently around HI scaling relations. This indicates that star-forming galaxies with low neutral gas content have a higher chance of emitting strongly in Lyα, but ultimately, neutral gas regulates the escape of Lyα emission on small scales.

21cm studies of both Lyα and LyC emitters conducted in this thesis have demonstrated that galaxy interactions play an important role in the escape of ultraviolet (UV) radiation from local galaxies. By perturbing the neutral gas content of galaxies and enhancing their star formation rate, these interactions are interesting mechanisms that facilitate the escape of UV radiation. According to cosmological models, galaxy mergers occurred more frequently in the early universe. Assessing the contribution of environment and galaxy interactions at high redshift will be essential to fully understand the first billion years of our universe.