Most urban wildlife have adapted to city living and generally tend to look for food where it is most plentiful and easy to access, and that would be your garbage! Two very common problems are also the easiest to fix.
Raccoons in dumpsters. Dumpsters are a cornucopia of tasty meals for these omnivores, and they are smart enough to know that an open dumpster is an invitation to dinner. They are excellent climbers and easily climb up and into the dumpster. The only problem is when the dumpster is near empty and they are unable to climb back out. Putting something in the dumpster, like a board or branch for them to climb out on will allow them to escape on their own. The corner of an old sheet or blanket can be secured to the outside and the rest left to hang inside the dumpster also. In the image below, there are 2 furry bodies curled up in the middle of a pile of plastic while they patiently wait for nightfall to climb out on the board I provided.
The best way to fix this problem is to make sure the dumpster has lids and that they are secured properly after you throw your garbage in there.
Possums in barrels. This is basically the same issue as the raccoons in dumpster, but on a smaller scale. If the barrel is empty enough, they can not climb back out. All you have to do is tip the barrel over and leave it for a while. Some may run out right away, some may not. If they are not gone by evening, they will most definitely be gone by morning. Sometimes they are literally "playing possum". It is an involuntary response where they act and look dead and can even smell like it sometimes. This trance can last up to 4 hours. Once the area is quiet they will make their escape under cover of darkness.
I know possums look very intimidating, especially with that mouthful of teeth, but they are actually very gentle souls. Contrary to popular belief, they do not go after people or pets and are not going lunge at you when you tip the barrel over. In the image below, 2 possums got themselves stuck in a barrel. I gently lifted them out and sent them on their way.
Once again, keeping a lid on your barrels will go a long way to preventing wildlife from getting in to them. You can secure them with bungee cords to keep the very crafty raccoons from opening them and getting in. Sometimes even that does not deter a hungry raccoon though. Sometimes it is best to wait until the day of collection to put your garbage out.