Galaxies with strong Lyman-alpha (Lya) emission line (also called Lya galaxies or emitters) offer an unique probe of the epoch of reionization - one of the important phases when most of the neutral hydrogen in the universe was ionized. In addition, Lya galaxies at high redshifts are a powerful tool to study low-mass galaxy formation. Since current observations suggest that the reionization is complete by redshift z~ 6, it is therefore necessary to discover galaxies at z > 6, to use their luminosity function (LF) as a probe of reionization. I found five z = 7.7 candidate Lya galaxies with line fluxes > 7x10-18 erg/s/cm/2 , from three different deep near-infrared (IR) narrowband (NB) imaging surveys in a volume > 4x104Mpc3. From the spectroscopic followup of four candidate galaxies, and with the current spectroscopic sensitivity, the detection of only the brightest candidate galaxy can be ruled out at 5 sigma level. Moreover, these observations successfully demonstrate that the sensitivity necessary for both, the NB imaging as well as the spectroscopic followup of z~ 8 Lya galaxies can be reached with the current instrumentation. While future, more sensitive spectroscopic observations are necessary, the observed Lya LF at z = 7.7 is consistent with z = 6.6 LF, suggesting that the intergalactic medium (IGM) is relatively ionized even at z = 7.7, with neutral fraction xHI≤ 30%. On the theoretical front, while several models of Lya emitters have been developed, the physical nature of Lya emitters is not yet completely known. Moreover, multi-parameter models and their complexities necessitates a simpler model. I have developed a simple, single-parameter model to populate dark mater halos with Lya emitters. The central tenet of this model, different from many of the earlier models, is that the star-formation rate (SFR), and hence the Lya luminosity, is proportional to the mass accretion rate rather than the total halo mass. This simple model is successful in reproducing many observable including LFs, stellar masses, SFRs, and clustering of Lya emitters from z~ 3 to z~ 7. Finally, using this model, I find that the mass accretion, and hence the star-formation in > 30% of Lya emitters at z~ 3 occur through major mergers, and this fraction increases to ~ 50% at z~7.