General:
* Reconstruction
* Replication
* Reproduction
* Recreating
* Living history
* Historical simulation
* Role-playing
More specific:
* Re-enacting (verb)
* Re-enactment event
* Historical event
* Battle reenactment (for historical battles)
* Civil War reenactment (for specific events)
The best word to use will depend on the specific situation. For example, if you are talking about a historical event, "reenactment" is probably the best word. If you are talking about recreating a scientific experiment, "replication" might be more appropriate.