Lookback is defined as the ability of a logical process to change its past locally (i.e. without involving other logical processes). Logical processes with lookback are able to process out-of-timestamp order events, enabling new synchronization protocols for the parallel discrete event simulation. This technology is directed to two of such protocols, LookBack-Global Virtual Time (LB-GVT) and LookBack-Earliest Input Time (LB-EIT), which are presented and their performances on the Closed Queuing Network (CQN) simulation are compared with each other. Lookback can be used to reduce the rollback frequency in optimistic simulations. The relation between lookahead and lookback is also discussed in detail. Finally, it is shown that lookback allows conservative simulations to circumvent the speedup limit imposed by the critical path.