Physics Potential of Future Atmospheric Neutrino Searches

The potential of future high statistics atmospheric neutrino experiments is considered, having in mind currently discussed huge detectors of various technologies (water Cerekov, magnetized iron, liquid Argon). I focus on the possibility to use atmospheric data to determine the octant of $\theta_{23}$ and the neutrino mass hierarchy. The sensitivity to the $\theta_{23}$-octant of atmospheric neutrinos is competitive (or even superior) to long-baseline experiments. I discuss the ideal properties of a fictitious atmospheric neutrino detector to determine the neutrino mass hierarchy.