When testing emails, when your application is the sender of the email, then tools like mailtrap are good for capturing the SMTP emails from Development and Staging environments, allowing automated tests to grab the emails and check things like the password reset flows.
Problems arise however when other systems are sending emails that are relevant to your application. A recent example I ran across was similar to this One Time Passcode workflow documented by Microsoft. The basic problem is that a third party is emailing to one of your test accounts and you need to extract some information from that email in order to complete an action.
As a tester, it is normally feasible to get a few test accounts setup by you email admins, and then your test cases can reuse that limited set of email addresses for the automated tests. A better way though is to use a service like Mailinator which allows easy access to a reasonable number of randomly generated usernames, say lmykuhuzgfbgim@mailinator.com, on one of the Mailinator domains. On the free tier, the emails show up in a public email box at https://www.mailinator.com/v4/public/inboxes.jsp?to=lmykuhuzgfbgim.
The fun starts as soon as you have an account, then you can use an API to get the contents of your private emails to your own mailinator domain. The Message API allows you to fetch the message identifiers, read the email related to that identifier and then delete the message related to that identifier to keep the mailbox clean.
The way this works is by specifying a wildcard catch-all on the email domain, that will catch all emails not addressed to known usernames. Normally an email server would send back a message saying mailbox not known, but the catch-all just grabs all those unknown emails and forms the basics of the mailinator system. You could roll your own, but much simpler to use Mailinator or one of the competing services.