In Apple Mail, the simple solution is to create a new mailbox (Mail > New Mailbox) called, for example, Newsletters. Then create a Rule that will filter incoming emails to that folder. To create a Rule, go to Mail > Preferences and tap Rule to the far right of the menu.
Tap the Add Rule button and give your Rule a name, such as Newsletters. Now to add a ‘condition’.
One option is to add the email address of each incoming newsletter like this: Under ‘If any of the following conditions are met’ use the default From and Contains, then add the address to the right. Tap the + button to add more addresses.
A simpler and quicker method is to filter messages that contain words common to email newsletters - like those in the unsubscribe message at the bottom.
Follow the above steps but select Message Content in the Condition drop-down, followed by Includes. In the text box add: Unsubscribe. Then tap + to add additional conditions with Un-subscribe and Subscription (not case sensitive).
Under ‘Perform the following actions’, choose ‘Move message’ to mailbox ‘Newsletters’ (or whatever you called the mailbox). Click OK and your newsletters should now appear in a separate folder.
… and in Gmail? Plain sailing ⛵️