IceCube and ANTARES are the world-largest neutrino telescopes. They are successfully taking data, producing a wealth of scientific results. Whereas their main goal is the detection of cosmic neutrinos with energies in the TeV-PeV range, both have demonstrated their capability to measure neutrino oscillations by studying atmospheric neutrinos with energies of 10-50 GeV. After recalling the methods of these measurements and the first published results of these searches, the potential of existing, and planned low-energy extensions of IceCube and KM3Net are discussed. These new detectors will be able to improve the knowledge of the atmospheric neutrino oscillation parameters, and in particular they might help to understand the neutrino mass hierarchy. Such studies, which use atmospheric neutrinos, could be complemented by measurements in a long-baseline neutrino beam, which is discussed as a long-term future option.