When using generated email addresses with G Suite (Google Apps) and Postmark, you can process incoming emails efficiently by setting up a catch-all address in your G Suite account. This allows you to route emails to the right place based on their local-part and from address. By configuring routing settings in the Google Admin portal and creating an inbound forwarding rule, you can forward emails from your catch-all address into Postmark's server. In Postmark, you set up an inbound webhook to deliver incoming emails as JSON data to your product. To process these emails, you need to parse the incoming Postmark webhook, which involves inspecting the "To" value of the email and using a specific header named X-Gm-Original-To to determine the true "To" address. With this setup, you can automate tasks such as updating issues in an issue tracking tool or processing job applications in a job applicant tracking tool.