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.