This is a review paper on the mixed-phase wavelet estimation using high-order statistics. We use an iterative linear inversion method as a primary thread, stringing together others including the maximum time-delayed moment (MTM) method and the normalized cumulant (NC) method. Both MTM and NC methods are not stable, because they make use of only single high-order-statistics slices. As for the iterative linear inversion method, it is stable but needs a good initial model. Therefore, we adopt a hybrid strategy that uses the MTM or NC method to generate an initial estimate of the wavelet for the iterative linear inversion method. The real seismic data test has shown that all inversions with different initial models converge to the same result within allowable accuracy. Therefore, the iterative linear inversion method is applicable to real multi-channel seismic data for wavelet estimation.