Classical and quantum $f(R)$ cosmology: The big rip, the little rip and
  the little sibling of the big rip
  The big rip, the little rip and the little sibling of the big rip are
cosmological doomsdays predicted by some phantom dark energy models that could
describe the future evolution of our Universe. When the universe evolves
towards either of these future cosmic events all bounded structures and,
ultimately, space-time itself are ripped apart. Nevertheless, it is commonly
belief that quantum gravity effects may smooth or even avoid these classically
predicted singularities. In this review, we discuss the classical and quantum
occurrence of these riplike events in the scheme of metric $f(R)$ theories of
gravity. The quantum analysis is performed in the framework of $f(R)$ quantum
geometrodynamics. In this context, we analyse the fulfilment of the DeWitt
criterion for the avoidance of these singular fates.
