I recall a few years back doing some reading on an Airbus, they had an optional extra product called AIRMAN, which performed real-time monitoring of the airframe and systems.
I guess the engines are monitored by the manufacturer.... RR for example can monitor in real-time, and make remote parameter changes to ensure smooth running. This can happen at anytime, and without the crew knowing anything happened.
The rough and ready DH8-Q400 has a central diagnostic system, any system fault logged can be recalled by engineers. Even faults that don't present to flight crew.