Watching or observing someone or something carefully, especially over a period of time.
Surveilling can make people feel like they are being watched or that someone is being sneaky.
Examples:
The detective is surveilling the suspect.
She is surveilling the area for any signs of danger.
The security camera is surveilling the store.
The cat is surveilling the mouse.
He is always surveilling his neighbors.
The robot is surveilling the room all day.