Convert the newsletters into RSS or Atom Feed with the free online tool Kill-The-Newsletter.
This tool creates a random email address to subscribe to your desired newsletter. To see those newsletters, add the provided feed link to your RSS reader.
This read-it-later app automatically moves your newsletter to its inbox. (you need a Gmail account for it) → Matter
Sick of newsletters? Get only the best issues from the best newsletter based on your day-by-day choices and changing interests. → Refind