I've often heard stories talking about how you could start smelling the cities from miles away, how people would defecate and urinate into the rivers, how people would toss buckets of their waste onto the street. How true is all this and how much did this lack of hygiene differ between century?
Better in some ways than it is stereotypically thought to be and worse in ways people don't usually think of.
In terms of what first comes to mind, bathing, tooth brushing, restroom hygiene, ect... they were not too behind the times. These things were normal for most people, and done on a semi regular basis. In fact, they were some of the first people to use soap and cleanliness was something that was valued.
Where they did lack heavily was non-personal hygiene. Things like waste disposal, cleaning houses and floors and whatnot were very bad. No one really had or used clean trash disposal systems. You just finished gutting a pig? Throw it out your front door and don't give it a second thought. Your animals filled your barn with manure or your dog just went number two in your house? Throw it outside and throw some good smelling herbs down to cover the smell.
Here is a quote from famous humanist and reformer Erasmus:
"The doors are, in general, laid with white clay, and are covered with rushes, occasionally renewed, but so imperfectly that the bottom layer is left undisturbed, sometimes for twenty years, harbouring expectoration, vomiting, the leakage of dogs and men, ale droppings, scraps of fish, and other abominations not fit to be mentioned. Whenever the weather changes a vapour is exhaled, which I consider very detrimental to health."
A statement from English parliament in 1388 (also highlighted):
"Item, that so much dung and filth of the garbage and entrails be cast and put into ditches, rivers, and other waters... so that the air there is grown greatly corrupt and infected, and many maladies and other intolerable diseases do daily happen"
There is something important described in the first quote. He mentions "rushes", this is a type of plant that people used to cover floors in the medieval ages along with other good smelling herbs and hay. This posed a massive issue as people would never clean their floors, they would just cover them up more. So underneath the fresh and good smelling recently layered herbs, there could be years and years of dirt, feces, meat, and rotting plant life. So when it became damp from rain or there was lots of moisture, all of the bacteria would rise into the air and cause infections.
Hope this answer is satisfactory :
how people would defecate and urinate into the rivers, how people would toss buckets of their waste onto the street
Tossing your bucket out on the street while you're in a Medieval city? They'll fine you. You should've gone to the public toilet or 'necessary house' (London had thirteen) to do your business, assuming you didn't have an outhouse or latrine of your own.
Mind you, this is not to say that a Medieval city is as clean as a city of 2021, but they're not nearly as filthy as pop culture accuses them of. But there's only so much you can do, as u/sunagainstgold shows us with the case of Richard le Rakiere's untimely death.
And as ever, if anyone would like to address the matter of Medieval urban sanitation (especially for places not London), don't let this linkdrop stop you! More insight is always welcome from anyone who has it.