  A core-collapse supernova (SN) releases almost all of its energy in the form
of neutrinos, which provide a unique opportunity to probe the working machinery
of a SN. These sites are prone to neutrino-neutrino refractive effects, which
can lead to fascinating collective flavour oscillations among neutrinos. This
causes rapid neutrino flavour conversions deep inside the SN even for
suppressed mixing angles, with intriguing consequences for the explosion
mechanism as well as nucleosynthesis. We review the physics of collective
oscillations of neutrinos -- both slow and fast, along with the well-known
resonant flavour conversion effects, and discuss the current state-of-the-art
of the field. Furthermore, we discuss how neutrinos from a SN can be used to
probe novel particle physics properties, extreme values of which are otherwise
inaccessible in laboratories.
