Do Neutrinos Violate CP?

In trying to answer the question in the title of my talk, I have argued on ground of naturalness that leptonic CP violation is very likely to exist both in the form of the Kobayashi-Maskawa type and the Majorana type phases. The latter part of the argument has to be backed up by a general argument by Yanagida which states that neutrinos must be Majorana particles because our universe is asymmetric with respect to baryon number. The argument is reviewed. Since the naturalness argument raises the possibility of naturally small theta_{13} and theta_{23} - pi/4, I discuss possible experimental methods for probing into these two small quantities. They include recent proposal of the resonant nu_e-bar absorption reaction enhanced by the M"ossbauer effect which may allow extremely high sensitivity for not only theta_{13} but also Delta m^2_{31}. The issue of how to resolve the theta_{23} octant degeneracy is briefly discussed with emphasis on the atmospheric neutrino observation and the reactor-accelerator combined methods.