We separate paper, cardboard, glass (by color) [1], aluminium and plastics (PET). All of those are free to get rid of. Trash however is not and is charged at a high rate per bag.
Paper and cardboard go to several paper plants which re-use it to produce recycled paper items.[2]
PET is turned back into bottle and other items [3]
Aluminum is reused and saves more than 95% of the original energy required to produce it (as you said) [4]
2/3 of the glass collected is turned into new bottles. [5]
Trash is sent of to an incineration plant which produces electricity and heat [6].
[1] https://www.buelach.ch/fileadmin/_processed_/csm_2012_07Juli...
[3] https://www.petrecycling.ch
[4] http://www.swissrecycling.ch/wertstoffe/aluminium/
[5] https://www.stadt-zuerich.ch/ted/de/index/entsorgung_recycli...
[6] https://docplayer.org/docs-images/50/18262133/images/page_4....