Normally, property taxes and HOA dues are paid by the owner.
But, fines issued by the HOA for tenant conduct or for things the tenant is responsible to take of care can be passed through to the tenant. The tenant agrees to the HOA rules as a normal part of agreeing to lease the property.
The same thing holds true for abatement charges from city or county government. Even though these are similar to property taxes, the tenant may be responsible for the charge. For example, if your lease says you mow the lawn, you refuse to, and the city comes and mows it, you can bet that the owner will charge you for the abatement (which might be $200).
Your lease can contain language that you pay the taxes. It can also say that you pay usage fees or HOA dues. While this is not common, it does happen. So, before signing ask and read what you sign.