  After outlining some popular ways to go beyond the standard model so as to
generate non-zero but tiny neutrino masses, I focus on several typical seesaw
mechanisms and discuss how to get a balance between their theoretical
naturalness and their experimental testability. Besides possible collider
signatures at the Large Hadron Collider, new and non-unitary CP-violating
effects are also expected to show up in neutrino oscillations for type-I,
type-(I+II), type-III and double seesaws at the TeV scale.
