besiege
To surround and attack a place so it must surrender.
To besiege means to surround a place with armed forces in order to capture it or force those inside to surrender. When an army besieges a castle or city, they cut it off from the outside world, preventing food, supplies, and reinforcements from getting in. The goal is to wait until the defenders grow so weak and desperate that they have to give up.
Throughout history, sieges could last for months or even years. The attackers would camp outside the walls, sometimes building their own fortifications, while those trapped inside rationed their food and water. Medieval castles were designed with thick walls, moats, and stockpiles of provisions specifically to withstand a siege.
The word also describes being overwhelmed by persistent demands or troubles. A teacher might feel besieged by questions from thirty students all at once. A doctor's office could be besieged by patients during flu season. When reporters besiege a politician with questions, they crowd around her and press her from all sides, much like an army surrounding a fortress.
The key idea is being surrounded, trapped, or overwhelmed with no easy escape. Whether it's an actual military siege or just feeling besieged by homework and chores, the word captures that sense of pressure closing in from all directions.