In this talk，I will present a recent result on the index theorem for End-Periodic Toeplitz operators. This result can be viewed as a generalization of the theorem by Dai and Zhang for Toeplitz operators on manifolds with boundary and also an odd-dimensional analogue of the index theorem for end-periodic Dirac operators by
Mrowka-Ruberman-Saveliev. In particular，we find a new eta-type invariant in the result and we will show its relation with the eta-type invariant introduced by Dai-Zhang. The approach follows mainly the heat kernel method with a b-calculus-like modification. In the proof，we also introduce a b-eta invariant and a variation formula for it. This is a joint work with professor Guangxiang Su.
