Today, you may have seen this notification under your Google Analytics Admin section > Tracking Info > Data Collection:

Cross-device remarketing GA notification

Many of you have been waiting for this for so long!

Finally, advertisers will be able to re-target a user whatever the acquisition device.

Finally, we will be able to continue the conversation and stop assuming they never visited the site before, which sometimes could result in weird/annoying situations where, for instance a mobile user would be asked to complete his/her purchase while he/she actually just did it earlier on his/her desktop…

OK users still have to be logged-in to his/her Google account and allow Google to access their browsing activity for advertising purpose, but this is still a huge progress towards better, smarter retargeting.
User experience should be improved too!

Can’t wait to see that in action.

https://support.google.com/analytics/answer/7365094

Below the full message about this update:

GA Remarketing Update