Responsibilities are primarly managed in the context of a role. If you're not sure who holds (or should hold) the responsibility, you can create an unmanaged responsibility directly on the team.
Each responsibility has a given frequency (or alternatively "ongoing") explaining the expectation of how often the responsibility should be adressed.
The responsibilities are grouped by category when displayed. Here's an excerpt of the list of responsibilities from the team leader role:
Assigning someone to a role does not automatically ensure that the associated responsibilities are adhered to. People are busier than ever, so unless a responsibility has been properly automated as default behaviour, it can quickly be forgotten.
Use recurring allocations to make sure that a given individual has reserved time for a given responsibility.
The avatars in the list of responsibilities indicate which users (if any) that have recurring allocations for a given responsibility.
Click into the responsibility to see details of the associated recurring allocations.