1. Literally, surrounded by the armed forces of the military or police, unable to leave or escape. The city remained under siege for nearly three months. By the time they finally surrendered, their citizens were starved nearly half to death.

2. Facing increasing pressure or difficulty. The company's stocks have been under siege as news of the scandal continues to spook investors.

3. Subject to criticisms or personal attacks from various different sources or angles. I've been under siege lately, with people from around the company coming to complain about the software issue.