Sometime in the early 1990s I was awakened by loud rustling noises coming from my bathroom. I thought maybe my cat was getting into some sort of mischief, until I realized that she was curled up next to my pillow.
So I got up and wandered into the bathroom, and there was a young 'possum rummaging through the trash basket. It was startled by my presence and ran into the corner behind the toilet and pissed itself. I had to improvise some method to capture the animal and get it out of my apartment, so I grabbed a box and a broom, swept the 'possum into the box, closed the top, and carried it outside where I let it go. Then I went back in and mopped the floor where it had disgraced itself.
Months later I was awakened by a loud crunching noise coming from the kitchen, like a cat eating cat food only louder, and once again the cat was in bed with me. So I went to the kitchen, turned on the light, and there was another 'possum eating from the cat food bowl. I chased it around the kitchen until it stuck its head under an empty pizza box and stopped running. I guess it thought that if it couldn't see me, I couldn't see it. So I grabbed a pair of stainless steel kitchen tongs and picked it up by the tail and carried it outside. It clearly did not like being carried like that, and was swinging around trying to bite me or get free or something, but couldn't. The 'possum made an awful noise, like "eh! eh!" sounded like an old man trying to clear his throat. I dumped it in the front garden and it ran off.
That was over a decade ago, haven't had any more marsupial incursions since then. So how did they get in my apartment? Well, I have a habit of leaving the front door ajar so the cats can come and go as they please without waking me.