It seems Microsoft is encourage people to use the app outlook. The app is good, but I still need to sync the contact between my iphone and outlook to get my contacts number.
Spent some time to check this issue, here is the fix:

    Login to outlook.live.com
    In the browser, click on Settings icon (gear at top right) ; scroll down the Quick Settings panel and click on 'View all Outlook settings'
    In the pop-up window, select 'General'; 'Mobile Devices'
    Select the iPhone, note if you have more than one iPhone (e.g. an older device), select the 'Edit' icon (pencil) to check the details including the version, 'OK' to exit details
    Click on the 'Delete' icon (bin) to remove the device
    Power off the iPhone
    Power on the iPhone - device should attempt to re-register with Microsoft
    Open the iPhone Mail app and look for email with subject: "ACTION REQUIRED TO SYNC EMAIL" (note, this email won't appear in the online version of Outlook, only in the iPhone Mail app)
    Scroll down the message and click on: "Continue using this email app".