Although the neutrino oscillations are well established phenomenon, new and unusual effects of oscillations in matter still continue to emerge. Three such effects will be described which have applications to the solar, supernova and low energy atmospheric neutrinos.
(i) Various parametric effects induced by periodic modulation of matter potential will be presented. In particular, I will describe realization of the parametric resonance for neutrinos propagating in a flux of background neutrinos.
(ii) Oscillations in a multi-layer medium, like the Earth, can be treated as emission and superposition of the ``oscillation waves'' from borders between layers.
(iii) The attenuation effect related to the energy uncertainty in the oscillation setup will be explained.