Observations of the Lyman-$\alpha$ Universe

Hydrogen Lyman-$\alpha$ (Ly$\alpha$) emission has been one of the major observational probes for the high redshift universe, since the first discoveries of high-$z$ Ly$\alpha$ emitting galaxies in the late 1990s. Due to the strong Ly$\alpha$ emission originated by resonant scattering and recombination of the most-abundant element, Ly$\alpha$ observations witness not only HII regions of star formation and AGN but also diffuse HI gas in the circum-galactic medium (CGM) and the inter-galactic medium (IGM). Here we review Ly$\alpha$ sources, and present theoretical interpretations reached to date. We conclude that: 1) A typical Ly$\alpha$ emitter (LAE) at $z\gtrsim 2$ with a $L^{\ast }$ Ly$\alpha$ luminosity is a high-$z$ counterpart of a local dwarf galaxy, a compact metal-poor star-forming galaxy (SFG) with an approximate stellar (halo) mass and star-formation rate of ${10}^{8-9}{M}_{\odot }$ ($10^{10-11} M_\odot$)and$1-10 M_\odot$yr$^{-1}$,respectively;2)High-$z$ SFGs ubiquitously have a diffuse Ly$\alpha$ emitting halo in the CGM extending to the halo virial radius and beyond; 3) Remaining neutral hydrogen at the epoch of reionization makes a strong dimming of Ly$\alpha$ emission for galaxies at $z>6$ that suggest the late reionization history. The next generation large telescope projects will combine Ly$\alpha$ emission data with HI Ly$\alpha$ absorptions and 21cm radio data that map out the majority of hydrogen (HI+HII) gas, uncovering the exchanges of i) matter by outflow/inflow and ii) radiation, relevant to cosmic reionization, between galaxies and the CGM/IGM.