On Agile projects, the usual way of capturing a requirement is what is called a user story. A typical user story has the form of, “As an x, I want the system to do y, so that I can accomplish z.” For example, “As a customer, I want the system to provide a transaction history screen, so that I can review my previous invoices.”
User stories are generally finer grained, smaller than use cases. However, a use case might be composed from multiple user stories. A collection of logically related and sometimes interdependent user stories is also referred to as an epic.