What is the best app for reading and organizing all of your newsletter subscriptions?

I run into the same issue, but what I find helpful as a Gmail user is simply using inbox's bundling features instead. It collapses to a nice single entry to update you upon incoming newsletters or you can schedule out when you receive the bundle (once a day or once a week). Pretty similar to Unroll.me, but native to Inbox and you get all the additional cool features from Inbox.

I'm a huge Inbox fan (true story: I switched from Microsoft to Google mail services because of the release of Inbox— I was that impressed). You can create your own bundling rules / quasi-folders that can sort your newsletters into dedicated places in your inbox for you. From there, you can read them or delete them / mark them "done" en masse. It's super effective and allows you to reach the coveted #InboxZero so easily, and rewards you with a little sun animation when you do so!

Been using Inbox since I got to try the beta, haven't moved since. It's super simple and intuitive and makes the best out of your mail. As stated earlier by @colbyfayock and @katesegrin it's amazing. Try it to believe it :)

Definitely take a look at unroll.me. You can add all of your newsletter subscriptions to your "roll up" and then get them all in a single email at a certain time of the day.

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The best part is you get an email just for newsletters so you don’t have to tie them all to your real email

Inspiratio comes with your private email (or you can set up auto-forwarding from Gmail) and all your newsletter subscriptions end up in a dedicated clutter free app. Think of an podcast experience but just for newsletters.

Mailstrom is a great option, with a lot of Unroll.me-style features, without the "sells your personal information" revenue source (Mailstrom is something you pay for).

Fast and efficient tool to unsubscribe from newsletters / spams ! It will scan your mailbox and let's you unsubscribe in one click. Credential based system, you get a few tokens to test it (unsubscribing costs 1 token), then you can buy more. I found it really fast and efficient, it worked on all but one of the senders I tried it with.