  We present detailed predictions for the properties of Ly-alpha-emitting
galaxies in the framework of the Lambda-CDM cosmology, calculated using the
semi-analytical galaxy formation model GALFORM. We explore a model which
assumes a top-heavy IMF in starbursts, and which has previously been shown to
explain the sub-mm number counts and the luminosity function of Lyman-break
galaxies at high redshift. We show that this model, with the simple assumption
that a fixed fraction of Ly-alpha photons escape from each galaxy, is
remarkably successful at explaining the observed luminosity function of
Ly-alpha emitters over the redshift range 3<z<6.6. We also examine the
distribution of Ly-alpha equivalent widths and the broad-band continuum
magnitudes of emitters, which are in good agreement with the available
observations. We look more deeply into the nature of Ly-alpha emitters,
presenting predictions for fundamental properties such as the stellar mass and
radius of the emitting galaxy and the mass of the host dark matter halo. The
model predicts that the clustering of Ly-alpha emitters at high redshifts
should be strongly biased relative to the dark matter, in agreement with
observational estimates. We also present predictions for the luminosity
function of Ly-alpha emitters at z>7, a redshift range which is starting to be
be probed by near-IR surveys and using new instruments such as DAzLE.
