In this talk, we summarize some recently developed Newton-type methods for solving M-tensor equation. We first present a tensor splitting based approximate Newton method and its monotone convergence property. That method can be applied to find a nonnegative solution to an M-tensor equation where the constant term can be arbitrary. We then review two Newton methods for finding the unique positive solution of the M-tensor equation with positive constant term. Both methods are globally and quadratically convergent. At last, we show numerical performance of those methods.