Looking at the Wikipedia page for star forts, I see a lot of information about how effective the design was, that it repulsed attacks and withstood cannon fire, that whole cities incorporated the design at tremendous expense, and so on. It all makes the design look highly impressive and durable (at least, as wikipedia notes, until the invention of the exploding shell).
By contrast, medieval fortifications of comparable grandeur seem to have been taken by assault occasionally. There is a consistent theme to their assault in media portrayals: attackers could use siege towers and ladders to get on top of the walls, would tunnel underneath them, would destroy them with artillery, or would batter down the gates. None of that seems to be easily possible with star forts.
So did anyone manage to successfully assault one? What was the general protocol for taking a fortified city? Was this just starving people out, as one might expect, or was it possible for a significantly sized army to successfully overwhelm a fortress?
Attacking a star fort or similar fortification was a science in of itself, with very precise measurements and timings based on the size of the city, etc.
The basic devices for attacking were the sap and the parallel. A parallel is a long trench that runs parallel to the wall being besieged. A sap is a very thin zig-zag trench that advances towards the wall for a certain distance to allow the construction of an additional parallel closer to the wall. Heavy guns on each parallel cover the construction of the next one. When the parallels had been brought close enough to the fortification, the defenders would be stormed or battered into submission by heavy guns.
Offensive earthworks were generally impervious to gunfire from the city under siege. These tactics were effective because the saps were so narrow that defensive gunfire could not reliably interfere with their construction, which allowed men and material to approach the walls in safety.
That said it was still possible for the defenders to over-power parallels close to the wall- it depended on the resources available to both sides.
Attackers might also use mine galleries- digging under defensive positions with tunnels and planting vast quantities of explosives to blow up walls from underneath.
A great example of all of these things is the Siege of Sevastopol during the Crimean War which saw all of these tactics and many others carried out over the course of a two-year siege. The defenders, lead by General Todleben, even dug counter-saps and created counter-works of their own during the siege.
All my information comes from Alexander Kinglake's Account of the War in the Crimea.
I have a question as well, but more of a general siege warfare kind of question.
How did a besieging army cross a moat, and how would they bring down the doors? As well, before the advent of effective cannon artilery, were catapults and trebuche's ever used to actually bring down the walls?