  In the framework of Loop Quantum Cosmology, inhomogeneous models are usually
quantized by means of a hybrid approach that combines loop quantization
techniques with standard quantum field theory methods. This approach is based
on a splitting of the phase space in a homogeneous sector, formed by global,
zero-modes, and an inhomogeneous sector, formed by the remaining, infinite
number of modes, that describe the local degrees of freedom. Then, the hybrid
quantization is attained by adopting a loop representation for the homogeneous
gravitational sector, while a Fock representation is used for the
inhomogeneities. The zero-mode of the Hamiltonian constraint operator couples
the homogeneous and inhomogeneous sectors. The hybrid approach, therefore, is
expected to provide a suitable quantum theory in regimes where the main quantum
effects of the geometry are those affecting the zero-modes, while the
inhomogeneities, still being quantum, can be treated in a more conventional
way. This hybrid strategy was first proposed for the simplest cosmological
midisuperspaces: the Gowdy models, and it has been later applied to the case of
cosmological perturbations. This paper reviews the construction and main
applications of hybrid Loop Quantum Cosmology
