* For his criminal activity: "The notorious bank robber was finally captured after a year on the run."
* For a negative reputation: "The city's notorious traffic jams are legendary."
* For something infamous: "The notorious Black Death pandemic wiped out millions of people."
* For something widely known: "The notorious Mount Everest is the highest mountain in the world."
* For something known for a particular quality: "The notorious Italian chef is famous for his spicy dishes."
Remember, "notorious" usually implies a negative connotation, but can sometimes be used for something simply very well-known, even if not necessarily bad.