Apparently the only way to log inbound emails initiated by a Contact (i.e. emails that aren't a reply to a logged outbound email) is to forward the email to hubspotID@forward.hubspot.com. This is using Gmail integration.
Can you not tell when an inbound email is from an email address matching a Contact? And if so, can't you just log the email against the Contact? Our old CRM did this automatically. Using the Forwarding address is clunky and easy to forget to do.
There is an existing idea that complains the outlook sidekick plugin WAS automatically adding Contacts (https://community.hubspot.com/t5/HubSpot-Ideas/Only-log-emails-to-EXISTING-CRM-contacts/idi-p/188027) but it was adding everyone and they wanted it to stop.
This confused me as Hubspot Support said "...unless the contact is replying to an email that you sent them (that was logged) it will not be logged unless you use the forwarding address". She also said this by design otherwise EVERY email I get would end up in the database as a new contact. (Just as the other poster complained.) I don't see whay that has to be the case.
I woud like to automatically log all inbound emails of existing contacts. And for emails from someone not in the database, I'd like a prompt to add them as a Contact. Ideally I'd like to setup in advance how to deal with emails from unknown senders.