What is the equivalent of domain_get_domain()?
Finally worked out the following ...

$domainNegotiator = \Drupal::service('domain.negotiator');
$current = $domainNegotiator-&gt;negotiateActiveHostname();


There are other methods on the DomainNegotiator service that I thought should work, particularly getActiveDomain() and getActiveId(), but they didn't return the domain I was actually on like I thought they would.

It's still a bit confusing to me, but I made it work.

EDIT: 
@berramou 's answer below helped as well. Originally, I was looking for the Domain object (from the Domain Access module), but it turns out the host was enough to match a Domain reference on my entity.