The most successful besiegers were probably the Romans. It wasn’t so much the act of laying siege that caused cities to surrender, it was the utter, uncompromising determination of the Romans to see the siege through to the end, and the atrocities they would commit on the surrendering population that made them so successful. Surrender immediately and you don’t get enslaved or butchered… hold out and things will go very, very badly.

I don’t recall all the details but there was one siege in western Europe where the mayor of the town declared ‘you won’t take us: we have supplies for four years in our store houses’ to which the Roman commander replied ‘then we’ll take you on the fifth year.’

Or take Masada, a supposedly impregnable fortress built on a mountaintop. First the Romans built walls all the way around it, both to contain the Jewish ‘rebels’ but also to protect the Roman siegeworks from any potential rescue force. Then they just built a ramp. A massive, massive ramp, that reached all the way up to the fortress walls (which weren’t that strong because who builds a strong wall when your fortress is perched on top of a mountain?). Then they wheeled up some siege engines, smashed their way through the walls and discovered most of the inhabitants had commited suicide rather than face capture.