C1 to build or create again something that has been damaged or destroyed:
The post-war government had the enormous task of reconstructing the city.
to change a system or organization completely, so that it works more effectively:
They were given the task of reconstructing the city's public transport system.
C2 If you reconstruct something that has happened in the past, you combine a lot of information in order to get a complete description of what happened:
The police tried to reconstruct the crime using the statements of witnesses.