  Despite its great successes in accounting for the current observations, the
so called `standard' model of cosmology faces a number of fundamental
unresolved questions. Paramount among these are those relating to the nature of
the origin of the universe and its early evolution. Regarding the question of
origin, the main difficulty has been the fact that within the classical general
relativistic framework, the `origin' is almost always a singular event at which
the laws of physics break down, thus making it impossible for such an event, or
epochs prior to it, to be studied. Recent studies have shown that Loop Quantum
Cosmology may provide a non-singular framework where these questions can be
addressed. The crucial role here is played by quantum effects, i.e.\
corrections to the classical equations of motion, which are incorporated in
effective equations employed to develop cosmological scenarios.
  In this chapter we shall consider the three main types of quantum effects
expected to be present within such a framework and discuss some of their
consequences for the effective equations. In particular we discuss how such
corrections can allow the construction of non-singular emergent scenarios for
the origin of the universe, which are past-eternal, oscillating and naturally
emerge into an inflationary phase. These scenarios provide a physically
plausible picture for the origin and early phases of the universe, which is in
principle testable. We pay special attention to the interplay between these
different types of correction terms. Given the absence, so far, of a complete
derivation of such corrections in general settings, it is important to bear in
mind the questions of consistency and robustness of scenarios based on partial
inclusion of such effects.
