I'm based in New Zealand where the GDRP isn't a thing, but I basically have a widget in my blog where you can sign up for the posts to be emailed, or follow on Facebook, or blogger.
But in line with the new European Union (EU) General Data Protection Regulation (GDPR) from 25 May 2018. The Google Peeps have updated their systems to include the new GDRP terms and conditions (I can't see them in NZ, so there's a screenprint below to show the message they sent me!)
the link to Googles privacy details is here
the link for Amazon GDPR privacy details is here (I use Amazon Associate links, although to date its only generated less than $10 in 5 years so I tend to just use them in a hope that one day I may get a book to read using it!)
Your privacy is of utmost importance to us and your data has always been treated with care, in fact, I have never looked to see who subscribes (I don't know where the list is hidden!).
When you receive an email from the blog there will always be an unsubscribe link at the bottom of it which you can utilize if you wish to stop the emails.
I have found a page where you can apparently create custom code so I can add my own cookie banner, but for now, I am going to trust that Google has added this disclaimer.
Thank you for your continued support.
Kat & Jenni