Vercel has introduced a new feature that allows users to apply custom domains to their preview deployments using branch domains. To set up this feature, users must first link their project to a Git repository and then add a new domain, selecting a specific Git branch to assign the domain to. Once the setup is complete, pushing a new commit to the selected branch will update the domain to reflect the latest deployment. This feature aims to provide users with more control over their branding and customization options for preview deployments.