Auditing provides vital information for diagnosing problems or investigating security breaches.
Most operating systems provide an audit mechanism that records information about system events. This can include basic information like keeping a record of sign on attempts, but it might also be possible to capture more detailed information like recording each command that is invoked or each file that is accessed.
Make sure that logging and auditing are properly tuned to record an appropriate amount of information without impeding system performance. You might also want to ensure that system logs are recorded locally and sent to a remote system to ensure higher availability and to reduce the likelihood that an attacker who gains access to the system will be able to cover their tracks.