When faced with a siege, there are three main ways to resolve it

1 A negotiated settlement, a direct assault or starvation (of the defenders). The negotiated settlement happened more often than you might think. Garrisons rarely wanted to die for the cause but, if they could hold out for relief, there was every reason to sit behind their thick walls and wait it out. The rules of sieges may sound barbaric now, but they served a purpose in their day. If the defenders gave up their fortifications, they could expect to leave with their honor and pretty much anything they could carry. However, if they resisted and the attackers finally breached the walls, they could expect no mercy. There is a brutal logic in this because it encouraged defenders to come to the negotiating table to avoid unnecessary bloodshed.

2 Starvation was a long, slow process. If any supplies were to get behind the walls, the siege would simply go on for much longer. Basic hygiene, as it was understood at the time, had to be observed both inside the fortifications and outside by the besiegers. An outbreak of diseases such as cholera could annihilate the attacking forces far more efficiently than any attack from inside the walls. However, if the besiegers could surround a city and if they had time on their side, this was a low-risk strategy and a guaranteed way to win. Starvation worked better with cities because there were more mouths to feed, and no amount of bravery offers protection from hunger. This kind of tactic (used for thousands of years by most civilizations) is now considered to be a war crime due to the disproportionate suffering of civilians.

3 A direct assault was always the least preferred option. Defenses are never impenetrable, and it was the job of defensive architects to work out how many men it would take to kill one member of the garrison. These multipliers meant that some sieges, with barely more than a hundred men, could successfully see off tens of thousands of the enemy. To get past these defenses an entire martial art form evolved. Tunneling under the walls of a city was a technical and dangerous business, but once the shafts were collapsed, the walls would usually come down with them. Then there were the highly sought-after giant siege engines, designed to rain down projectiles, anything from rocks, to pots of Greek fire, to diseased animals (to spread pestilence within). Later, cannons were used to batter the stone walls of these citadels. There were also giant siege towers, designed to roll up to the walls and allow easy access for attackers. Siege ladders, battering rams … the list of siege machines and weapons goes on and on. All of these were extremely expensive in terms of materials, resources and men’s lives.

Yes, there was always subterfuge, but that wasn't always a likely option but the complexities of above show you why the Middle Ages are sometimes referred to as the era of siege warfare.