General:
* Intelligence gathering
* Spying
* Secret service
* Covert operations
* Undercover work
More formal:
* Counterintelligence
* Strategic surveillance
* Foreign intelligence
* National security
Informal:
* Snooping
* Eavesdropping
* Sussing out
Other options:
* Recon (short for reconnaissance)
* Infiltration
* Subversion
The best synonym for espionage will depend on the specific context of your writing or conversation.