Spy on
Definition 1 of 2
Pro Tip 1/3Privacy Invasion
The phrase implies an intrusion into someone's private life without consent, often negatively received. 
He felt uneasy knowing his boss might spy on his social media profiles.
Pro Tip 2/3Secretive Intent
Use when the observer doesn't want to be noticed, intending to keep their observation hidden. 
She pretended to read the newspaper to spy on the conversation next to her.
Pro Tip 3/3Information Gathering
Often used when the purpose is to collect information for personal use or advantage. 
Companies shouldn't spy on customers to get confidential data.