Nebular emission-lines offer a powerful tool for studying the physical properties and chemical compositions of galaxies in the near and distant universe. They are excellent tracers of star formation activity in galaxies as well as efficient probes of intergalactic medium in the early universe. This dissertation presents findings from three different studies of emission-line galaxies (a.k.a. line emitters) at low and high redshifts, based on imaging and spectroscopic observations. The first study explores Hα emitters at z ~ 0.6 from the Cosmic Deep And Wide Narrow-band (DAWN) survey, providing robust measurements of the Hα luminosity function (LF) and the star-formation rate density (SFRD) at z ~ 0.6. The effects of different dust-extinction corrections on the measured LF were also investigated in this study. Owing to the observing strategy employed in this survey, this study demonstrates the importance of performing deep and wide-field observations, in order to robustly constrain the entire LF. In the second study, 21 Lyman-α emitter (LAE) candidates at z ~ 7 from the Lyman-Alpha Galaxies in the Epoch of Reionization (LAGER) survey were followed up spectroscopically, using Low Resolution Imaging Spectrometer (LRIS) on the Keck telescope. 15 of these were confirmed to be LAEs, obtaining a spectroscopic confirmation success rate of ~ 80% for LAGER LAE candidates. Apart from Lyman- α, no other rest-frame ultra-violet (UV) nebular lines were detected, with a 2σ upper limit for the ratio of NV/Lyα ≲ 0.27. These confirmations help validate the neutral Hydrogen fraction estimates from LAGER, which is consistent with a fully ionized universe at z ~ 7. The final study investigated the presence of black hole/active galactic nuclei (AGN) signatures among Green Pea (GP) galaxies, using mid-infrared (MIR) observations from the Wide-field Infrared Survey Explorer (WISE) mission. 31 GPs were selected as candidate AGN based on a stringent MIR color-color diagnostic including two GPs exhibiting notable variability in the shorter two WISE bandpasses. Given that GPs are one of the best analogs of high-redshift galaxies, findings from this study suggest that AGN activity could be responsible for the hard ionizing radiation observed in some GPs, which has crucial implications on the sources likely to have contributed towards cosmic reionization.

One of the most fundamental questions in astronomy is how the Universe evolved to become the highly structured system of stars and galaxies that we see today. The answer to this question can be largely uncovered in a relatively unexplored period in the history of the Universe known as the Epoch of Reionization (EoR), where radiation from the first generation of stars and galaxies ionized the neutral hydrogen gas in the intergalactic medium. The reionization process created "bubbles" of ionized regions around radiating sources that perturbed the matter density distribution and influenced the subsequent formation of stars and galaxies. Exactly how and when reionization occurred are currently up for debate. However, by studying this transformative period we hope to unravel the underlying astrophysics that governs the formation and evolution of the first stars and galaxies.

The most promising method to study reionization is 21 cm tomography, which aims to map the 3D distribution of the neutral hydrogen gas using the 21 cm emission lines from the spin-flip transition of neutral hydrogen atoms. Several radio interferometers operating at frequencies below 200 MHz are conducting these experiments, but direct images of the observed fields are limited due to contamination from astrophysical foreground sources and other systematics, forcing current and upcoming analyses to be statistical.

In this dissertation, I studied one-point statistics of the 21 cm brightness temperature intensity fluctuations, focusing on how measurements from observations would be biased by different contaminations and instrumental systematics and how to mitigate them. I develop simulation tools to generate realistic mock 21 cm observations of the Hydrogen Epoch of Reionization Array (HERA), a new interferometer being constructed in the Karoo desert in South Africa, and perform sensitivity analysis of the telescope to one-point statistics using the mock observations. I show that HERA will be able to measure 21 cm one-point statistics with sufficient sensitivity if foreground contaminations can be sufficiently mitigated. In the presence of foreground, I develop a rolling foreground avoidance filter technique and demonstrate that it can be used to obtain noise-limited measurements with HERA. To assess these techniques on real data, I obtain measurements from the legacy data from the first season observation of the Murchison Widefield Array (MWA) and perform additional high-precision radio interferometric simulations for comparison. Through these works, I have developed new statistical tools that are complementary to the power spectrum method that is currently the central focus of the majority of analyses. In addition to confirming power spectrum detections, one-point statistics offer additional information on the distribution of the 21 cm fluctuations, which is directly linked to the astrophysics of structure formation.