The eta-invariant was introduced in the 1970’s by Atiyah-Patodi-Singer as the boundary contribution of index theorem for compact manifolds with boundary. It is formally equal to the number of positive eigenvalues of the Dirac operator minus the number of its negative eigenvalues and has many applications in geometry, topology, number theory and theoretical physics. It is not computable in a local way and not a topological invariant. When there is group action, we can define the equivariant eta-invariants. In this talk, we will give a general introduction on eta-invariants, and at the end, we will explain our joint work with Bo Liu: a localization formula for equivariant eta-invariants, i.e., understand the equivariant eta-invariant via the contribution of the fixed point sets of the group action.