We present a classification that groups lookback into four types: direct strong lookback, universal strong lookback, direct weak lookback, and universal weak lookback. They are defined in terms of absolute and dynamic impact times. We discuss relationships between lookback types by considering when rollbacks and/or antimessages are avoided. From different types of lookback, we also derive three optimization techniques for optimistic simulation and point out their advantages over lazy cancellation. Finally, we show that all four types of lookback exist in the PCS network simulation and can be exploited by either lookback-based or optimistic protocols.