Once you have organized your requests in folders, you can run any given sequence by clicking on it at the sidebar on the left. If everything is OK, you'll get green marks for all tests; a red mark highlights an issue:
Running a collection runs every test in it. Green blocks show successes; red ones mark errors.
With this, you already have a good tool for documenting your API (make sure that every test and field has an explanation) and for making sure that it keeps working, going beyond the unit testing into full end-to-end (E2E) testing.
Depending on your Postman account, you can also set things up to get periodical monitoring of your API; check out https://www.getpostman.com/docs/v6/postman/monitors/intro_monitors for more information.