With competent defenders, "the fast way" has a high failure rate. And even if successful, a high body count.

Or, if you're referring to gunpowder/cannon tactics - those are the reason for medieval-style fortifications falling out of favor, 1500 CE-ish.

Nope, I meant pre-gunpowder.

But as always, money can break any castle wall. But lobbing putrefied meat into wells, waiting out their stores, and so forth work.

Well constructed medevial fortresses imposed such a high cost on any attackers that were rarely attempts to assault them directly. There was almost always an easier way.

However if was a city or sometimes a large town, the calculus changes because the payoff was much higher. Also it may not have always been possible to wait the defenders out - because of relief armies and the troops getting restless and possibly deserting. An example in the "medevial" period (lets say ~1050-1453) where walls were directly attacked would be Jerusalem

I remember watching a video about a siege the Romans did, lasting a few years or so, where they built a whole friggin ramp up to the fortress, where otherwise they would only have had a thin path up, which would have been impossible to get siege towers and stuff up. Mind-blowing stuff.

Its quite fascinating and defensive innovations drove alot of interesting architechture. For example machiolations were a response to sapping being used especially by Saracen armies (who seemed to favor sapping more than Europeans) against the Crusaders.

Also the movement from square towers to round ones, once again as a defense for sapping, and displacing the tower from the wall or keep in order to be able to flank assaulters attempting an escalade.

The mastery of stone fortifications made walls nearly impregnable to breaches until cannons were developed, and even by then it was a dodgy proposiiton. For instance at Constantinople in 1453 the Turks had huge cannon which could damage the walls, yet it was not the reason the city fell. The defenders were able to repair the walls before the cannon could reload for a second shot. The reason Constantinople fell was a side gate was left open (either intentionally or accidentally) which allowed the Turks to pour through. There were alot of incidents like this such as the defenders of the Krak de Chevaliers (in modern day Syria) being duped into believing their commander had ordered their surrender

>Also the movement from square towers to round ones, once again as a defense for sapping

I thought the move to round towers was due to the increased effectiveness of canon.

Round towers and concentric design started to become popular in the 13th century which was well before cannon were useful. Cannon were not all that practical until the mid-15th century, which is when you started to see the "star" fort design, and the replacement of stone with earth and brick, lower walls that were more sloped.

You might be thinking of Masada: https://en.wikipedia.org/wiki/Siege_of_Masada?wprov=sfti1

Yes, that looks like the video I saw and the text seems to describe it.

After a three month siege in 1136, Exeter Castle finally had to surrender when they ran out of wine. O cruel fate.