Depends on the business and just how much if any of the rental property was involved.
For example running a website from a rental is fine.
But running something like a factory would be a major problem
And yes its in almost all tenancies that you CAN NOT run a business from the premises. (insurance would be invalid, and it could also be prohibited by local laws in some places.)
So as a general overall response as a landlord i would say you would be declined permission to run anything from a rental unless its web based or a small office in your home. But even a small office would require permission.
If you are referring to a residential rental property, the lease undoubtedly prohibits your use of the premises for business use....
LOTS of possible issues, from their carrier denying coverage following a loss to increase foot traffic, to zoning and taxes.
Does anybody run a business from a rental property? Is it something that landlords would be too fussy about? Any possible issues?