When Microsoft announced Your Phone at Build this year, it promised a window into your phone, complete with photos, messages, calls, and more. It was offered to Insiders in August, but it wasn't complete. It only allowed you to view your 25 most recent images on your Android phone.
Today, an update is rolling out allowing you to send and receive SMS messages from the Your Phone app. It should be available for all rings of the Insider Program that have a Your Phone app, and it might actually take a few minutes for Messages to show up after the app update is installed.
Unfortunately, it still only works with Android. When Your Phone is complete, iOS functionality will still be extremely limited. Even clients that support SMS for iOS - such as Dell Mobile Connect or HP WorkWise - require your iPhone to be awake before sending an SMS message, although some will let you input your PIN so it can wake up your iPhone for you. To be clear, this is a limitation on Apple's end, not Microsoft's.
Obviously, Microsoft is going to continue expanding the feature set of Your Phone, and eventually, it will roll out to Windows 10 version 1803 as well. For now though, Android users can play with SMS messaging.