What is prohibited
Fake reviews, bought reviews, undisclosed insider reviews, suppressing negative ones, and presenting a filtered set as the whole picture.
What is not
Asking your customers for reviews. Displaying a selection on your own site, provided the rating you show is the real one.
The gating confusion
Selective soliciting is not banned outright in the US. Suppression and misrepresentation are. Platform policy is the stricter constraint: Google discourages selective asking, Yelp forbids soliciting entirely.
Elsewhere
The UK regime is broader in places, and EU rules require traders to state how reviews are verified. Design around the strictest rule that applies to you.
Read the full version
The full summary is in the FTC rule on fake reviews. Not legal advice — have a lawyer read anything you rely on.