a military operation in which a city or fortified place is surrounded and, blockaded, and bombarded to compel it to surrender
a similar operation, e.g. by a police force, to force somebody to surrender
lay siege to
to besiege (e.g. a city) militarily
laid siege to the town
to pursue (somebody or something) diligently or persistently
[Middle English sege from Old French, ultimately from Latin sedēre to sit]