Studying the formation and evolution of galaxies, from the epoch of reionisation (EoR) to the present day, unveils a captivating narrative of cosmic history. Hydrogen Lyman-alpha (Lyα) emission is a critical probe for understanding the high-redshift Universe and a powerful tool to shed light on star-formation activities. Emergent Lyα spectra (single, double peak) provide useful hints on circumgalactic medium (CGM) gas kinematics and interstellar medium (ISM) structure. Further, the precise timing of reionization and sources capable of emitting sufficient ionising photons (Lyman-continuum or LyC photons) remain subjects of active debate till date. Direct observation of LyC photons is almost impossible at z > 4 due to strong intergalactic medium (IGM) attenuation. Lyα emission, however, serves as a reliable indirect tracer of LyC leakage. Using VLT/MUSE data, we have been studying Lyα emitting galaxies, known as Lyα emitters (LAEs) up to the edge of cosmic reionisation. Particularly, by simulating observed double-peaked profiles of Lyα emission using radiative transfer model, we have been investigating complex gas kinematics (inflows and outflows), ISM properties and conditions that lead to escape of both Lyα and LyC photons. We have also been investigating the survival of Lyα photons from luminous LAEs showing broad line profiles during the reionisation era. Our findings suggest that high-luminosity LAEs at z > 6 tend to reside in more highly ionised regions compared to lower luminosity LAEs, self-shielding them from IGM scattering. This study advances our understanding of the cosmic reionisation process in the Universe.