The fate of the phantom dark energy universe in semiclassical and loop quantum cosmology is investigated. In semiclassical cosmology, quantum corrections coming from massless fields conformally coupled with gravity are considered, to see if they can lead to avoidance of the Big Rip singularity, which shows up in a flat Friedmann-Robertson-Walker universe, filled with phantom dark energy and modeled by an equation of state of the form p = ωρ with ω < −1 (this model is justified by WMAP observations which indicate that ω = −1.10 ± 0.14 Komatsu (Astrophys. J. Suppl. Ser. 192:18, 2011). The dynamics of the model are discussed for all values of the two parameters, named α > 0 and β < 0, which come from quantum corrections. It is concluded that, when $${-1<\frac{\beta}{3\alpha} <0 }$$ , almost all solutions develop future singularities (the corresponding scale factor and energy density go down to zero in finite time). However, when $${-1>\frac{\beta}{3\alpha}}$$ , almost all solutions describe a universe bouncing infinitely many times (an oscillating universe). On the other hand, in loop quantum cosmology, the classical Friedmann equation can be replaced by the so-called tree-level Friedmann equation. This equation contains a term proportional to the square of the energy density which leads to the avoidance of the Big Rip singularity.