While I am experiencing the same issue as everyone else here, I want to add that messages on my iMac (Late 2015) running High Sierra Supplemental Update regularly take hours to download messages - not minutes.
For example, I shut down my iMac last night at bedtime; I turned it on several hours ago this morning and the Messages app still hasn't updated to include messages sent last night from my iPhone 7 Plus or iPad Pro (both running iOS 11.0.3).
For many weeks I adopted a new habit:
- restart the Messages app with no luck
- sign out of iCloud and sign back in with no luck
- restart my Mac with no luck
When I stop this idiotic and clearly useless behaviour and accept that Messages is broken, I'll acknowledge that I've reached a new milestone as a Mac user: This is the sort of user experience I have with Windows 10 and Android.
For 25+ years I didn't expect this on a Mac but since 2011 I've become accustomed to it. Being loyal and waiting for something better hasn't paid off!
With my age and lifestyle, I'll probably be dead before the gap grinds shut, but what if I'm not?! Will I spend my final years grappling with a switch to Windows and Android? Kill me now!