Email service to do advanced mailings than MailChimp is capable of?

We've been using MailChimp for a long time to send our email newsletters. While it allows for some general segmentation of your list, we need a solution that allows us to trigger emails based on specific actions in our business.

For example, for a B2C site, we want to trigger an email to inactive users who haven't logged in for X number of days.

What are some email providers that can offer this level of customization and integration?

I've looked at some MailChimp competitors like CampaignMonitor, but none of them offer this level of integration. Any suggestions?

Mailchimp can send an email to whatever group of people you tell it to.

There's the clue - it's not designed to be a business rules engine that checks your system for triggers. Instead, your system should be able to generate a list of inactive users (this should be a fairly trivial piece of code/script for a techie to write, even with a batch job to run on a frequent basis). Export that list to Mailchimp, and keep going as you were.

SendGrid might be easier to integrate, but either way, you're going to have to create some code on your end to create the triggers.

There's no perfect solution that wouldn't require some integration from your end.

For your use case, Exact Target sounds more like what you need, not MailChimp.

A newer startup offering a solution to this is Customer.io.