Is a landlord responsible for his tenants' actions?

In what cases can a landlord be held responsible for actions of his tenants?
This keeps coming up for a friend of mine who owns a rental property next to another rental property owned by a friend. One renter in each property. When the renters don’t get along and one starts being annoying or abusive in one way or another, the tenants tend to start complaining to one or both landlords seeing if they can get any leverage, and sometimes implying that the landlord is responsible for the alleged actions of their tenant.
I wonder if the landlord has any responsibility other than to make reasonable communications and requests to keep the peace. Does anyone here know the actual legal limits of a landlord’s responsibility for his tenants’ actions? If a tenant does damage to a neighbor, can the landlord be held accountable, and in what circumstances?