Notifications (which are announced by a "bing" sound and a glowing yellow ring, and you listen to by saying, "Alexa, what are my notifications") can be pushed to your Alexa device using a skill I created called Notify Me and a REST API.
Notify Me works great with IFTTT via its Webhooks service. First, of course, you have to enable the Notify Me skill; then launch the skill to get an access code (say, "Alexa, launch Notify Me" and the skill will email you the access code). Next, you fill out the IFTTT Webhooks service like this...
URL: https://api.notifymyecho.com/v1/NotifyMe
Method: POST
Content Type: application/json
Body: {"notification": "HOWDY", "accessCode":"ACCESS_CODE"}
...replacing HOWDY with the actual message you want to send (it does not have to be all uppercase, of course) and replacing ACCESS_CODE with the access code you previously received via email.
See www.notifymyecho.com for more info.