This, like any form of sponsorship, involves getting advertisers on board to give you money in return for exposure to their brand/website/products/services. If you send out a regular newsletter or just have a large mailing list, you can sell sponsorship.

This could involve the sponsor being mentioned within the newsletter somewhere via a banner or text link.

Advantages: Once you have acquired sponsorship, it's really easy to implement this into your newsletter.

You can offer various sponsorship packages to bring in even more revenue from your mailing lists that can include being a 'topic/category sponsor' (i.e. they sponsor newsletters that go out about a specific topic).

Disadvantages: It isn't always simple to gain sponsors in the first place. Unless you have a large and engaging mailing list you're going to struggle. Even then, the revenue potential isn't always large and you may find that you lose out some of the click-throughs to your website via the sponsor's link.