When was the siege towers and trebuchets (sp?) used for the last time?

Siege towers were recorded as being used at Constantinople in 1453 but were starting to become obsolete even then. A version fitted with cannon was used at the siege of Kazan in 1552, but they all but died out after that.

Trebuchets were also replaced by cannon, although there is a record of one with a 33ft arm being ordered by Napoleon III, the last monarch of France, in the mid 1800s.

I think that 'the_lipsiot' has given you a great answer, especially concerning the Siege Towers part of your question.

He is also correct in singling out Napoleon III's contraption as (probably) the very last Trebuchet to be designed with warfare in mind ... although I don't believe that it actually saw any active service.

But a Trebuchet is just a sophisticated Catapult, and there have certainly been others of those since the time of Napoleon III.

In World War One on the Western Front, when the armies quickly found that they had to dig trenches and take shelter in them, hostilities became siege warfare, not a war of movement. The German army, as usual, came well prepared for every eventuality, replete with mortars and hand grenades. These weapons were essential components for success in trench warfare; but at first the British army had neither; the French army had a few antique mortars. Needing to improvize something to counter the Germans' initial total superiority in proper mortars and grenades, both the British and the French developed temporary (and inferior) solutions. They made up "grenades" from empty meat and jam cans, stuffed with explosive and ignited via time fuses: a small-scale and primitive version, if you like, of the IED's still being used in Iraq and Afghanistan. And to hurl these "grenades" beyond the range of a human throw, they built for themselves Catapults that could be fired from the floor of their trenches. See link [1] for a photo.

I also believe that, until they were banned not very long ago due to a number of fatalities, macho thrill-seekers in Britain were engaging in the extreme sport of being launched from large Trebuchet-Catapults to land (if they were lucky) in safety nets.

The trebuchet was last used by the defenders during the siege of Rhodes by the Turks in 1480. Powder inside Rhodes was running low and when one of the besieged, a Basque, said he knew how to build a trebuchet, they took him up on it.

right before cannons and explosive charges were invented