Accelerated Expansion of the Universe as a Quantum Gravity Phenomenon

We have known approximately 100 years that the Universe is expanding. But the striking discovery came at the end of 20th century, when we found that it is expanding with acceleration. Since then, many models have been developed in cosmology to explain this phenomenon. One of the possible elucidations is that the theory of gravity must be modified at the classical level. But many such models were already excluded by the gravitational wave experiments. Therefore, we must slowly start to ask a much more urgent question: could accelerated expansion of the Universe be a phenomenon of quantum gravity ? We review the basic models of how we explain the origin of dark energy or the cosmological constant in metastring theory, discrete approaches to quantum gravity, group field theory, non-commutative geometry, causal dynamical triangulation, asymptotic safety, models based on holography and entropic gravity. We mention at the end a newly formed approach to the quantization of gravity, the ring paradigm, which would, just after the application to cosmology, naturally model the late-time accelerated expansion epoch in the Universe. But what is completely striking is that the final formulation of this theory would ultimately solve the old problem of the cosmological constant.