Use a Custom Domain to send Emails with Mailgun

This is something pretty straight forward. There are two options for you to do that.

Use the API

Send a Basic Authenticated POST request with from, to, subject and text in form-data to the URL shown. Use your own domain in the URL.

Note that Basic Authentication sends Base64 encoded username and password seperated by a colon as the Authorization header.

Use an SMTP Client

The other option is to use an SMTP Client. Your SMTP credentials will be there under your domain.

No Incoming Mail Server Support in Mailgun

I noticed that Mailgun does not have POP3/IMAP. Therfore only option to receive emails will be by forwarding the emails to an existing inbox.