  We review some theoretical and statistical aspects of the origin of the
large-scale structure in the Universe, in view of the two most widely known and
accepted scenarios: the inflaton and the curvaton scenarios. Among the
theoretical aspects, we point out the impossibility of having a low
inflationary energy scale in the simplest curvaton model. A couple of
modifications to the simplest setup are explored, corresponding to the
implementation of a second (thermal) inflationary period whose end makes the
curvaton field `heavy', triggering either its oscillations or immediate decay.
Low scale inflation is then possible to attain with H_\ast being as low as 1
TeV. Among the statistical aspects, we study the bispectrum
B_\zeta(k_1,k_2,k_3) of the primordial curvature perturbation \zeta whose
normalisation \fnl gives information about the level of non-gaussianity in
\zeta. In connection with \fnl, several conserved and/or gauge invariant
quantities described as the second-order curvature perturbation have been given
in the literature. We review each of these quantities showing how to interpret
one in terms of the others, and analyze the respective expected \fnl in both
the inflaton and the curvaton scenarios as well as in other less known models
for the generation of primordial perturbations and/or non-gaussianities. The
\delta N formalism turns out to be a powerful technique to compute \fnl in
multi-component slow-roll inflation, as the knowledge of the evolution of some
family of unperturbed universes is the only requirement. We present for the
first time this formalism and apply it to selected examples.
