While (I imagine) most people living in the countryside just disposed of their excreta in a nearby water body or a farm or just near the wilderness, how did the people in more densely populated areas, like cities, deal with it? I can't imagine they were carrying their excreta to some place outside the city every day to throw it, nor can I imagine there being a sanitary way to dump it inside a city.
Was there a marked difference in this kind of waste disposal across different countries and continents, or did everyone deal with it similarly?
Also, what happened during a siege (in say a walled city or the people living inside a large castle) when it dragged on for years and there was no way to go outside?
More can always be said on that topic, but here are some links to previous answers collected by u/DanKensington. I also wrote a little about adjacent topics here (castle latrines) and here (composting methods and night soil collection). The takehome message is that people were always concerned about pooping in a clean fashion: there were facilities that allowed them to do so more or less privately, and systems to collect the night soil and recycle it (people were very much interested in recycling). The disposal of urine and fecal matter was still a ongoing problem in cities, though, due to the vast amounts of excrements produced and the difficulties (and costs) associated to their removal. Authorities, local to royal, tried to contain the flow as much as they could (French kings regularly published angry ordinances about this for centuries), until proper sewage management systems were put in place in the (late) 19th century.