In Denmark we call it "newsletters". To send out your newsletters, you need some software - and it's called "email marketing software"
When you first hear about "newsletters" you think "that's simple". It's anything but simple. Creating software that sends out emails is a rather complicated task. For example, they have to do their best to get through spam filters. It's not just one setting in the email - because if it was, the spammers would use that setting too. In addition, it must be easy to set up a newsletter, it must be flexible so that you can have buttons and images in it, and your newsletter must look good on mobiles, tablets and various email programs on the computer. It's not a simple task.
Add to that the fact that you want statistics on who opens and clicks. It should also be integrated with your webshop system so that those who sign up when they pay are automatically sent to your email marketing software.
Many email marketing software systems also offer what is called automatic emails. This means that you can set it up to send an email, for example, 1 hour after a user has signed up. Then 3 days, then 7 days etc. This way you can have a so-called "automation flow" running. An automation flow - or automatic emails (also called autoresponders) - is a really effective marketing channel as it only needs to be set up once. Then you benefit from everyone who signs up for your newsletter receiving your emails.
There are a lot of them out there. The best known is probably the American Mailchimp. In Denmark, one of the main players is Ubivox.
A third option is Australian Campaign Monitor
We've been working with online marketing ourselves for decades. As the only shop system in the country, we have spoken multiple times at conferences such as Marketingcamp, SEOday, Shopcamp, Digital Marketing, E-commerce Manager, Ecommerce Day, Web Analytics Wednesday and many more.