Cities become more and more vulnerable to espionage depending on their Intrigue level. The more Covert Operations that are sent against a city, the higher that area's Intrigue becomes. This increases the chance of success for additional attacks, and it also allows even more frightening missions to be attempted. Low Intrigue doesn't have any potential downsides for the city or its player; the Operations that are allowable at Intrigue Levels 1-3 have no deleterious effects for the City or player that they're unleashed against. It's at Intrigue Levels 4 and 5 that things go from annoying to scary.
To protect yourself from this threat, send your Agents to your own Cities. Agents placed on counterintelligence raise the chance of catching enemy Agents who are operating in that City, and your Agents also improve the rate that your City returns to a lower Intrigue level.

Use the Assignment screen to quickly look at all of your Cities, and send Agents to the Cities that have worrisome levels of Intrigue. You can also see the Intrigue level of a City in the City Manager. Open the City Manager and look at the row of five diamonds that is underneath the Border Growth indicator. The more diamonds that fill, the more Intrigue that city has. Beware!
Another way to reduce the effects of Intrigue is to construct Surveillance Webs in key Cities that are under frequent attack. These defensive buildings take the threat of serious covert attacks entirely off the table for the City in question, capping the City's Intrigue level at 3.
Counterintelligence has no negative consequences diplomatically. In fact, you can even score a few brownie points with other colonies. If you catch and kill their spies and then choose to forgive the transgressor, you gain a mild bonus with that sponsor in the future. That's pretty cool for doing something that helps you defensively anyway.
