  In this paper, we first show the well-posedness of the SDEs driven by
L\'{e}vy noises under mild conditions. Then, we consider the existence and
uniqueness of periodic solutions of the SDEs. To establish the ergodicity and
uniqueness of periodic solutions, we investigate the strong Feller property and
the irreducibility of the corresponding time-inhomogeneous semigroups when both
small and large jumps are allowed in the equations. Some examples are presented
to illustrate our results.
