When I receive a vCard (.vcf), Hangouts does not show the content of it! Is there a setting for this or simply this feature is omitted in Hangouts?
Here, in this picture I sent a vCard and the other persons sent another vCard. I cannot see the content of either of them.
And when I tap the message, I still cannot see the content from there.
Android doesn't have native support for vCards and it's annoying. Fortunately, since they come through as SMS/MMS messages they aren't only in Hangouts, any SMS/MMS-handling app you install can read the messages so long as you haven't deleted them. You can install bizcardmanager (it's $1.50 but there's a free version too) and it will show a list of vCards received via SMS and you can import them to your contacts from there. There are other apps which claim to share contacts, not all work very well. I recommend bizcard (I have nothing to do with the app or its developer) simply because I know for a fact that it works.
Not a great solution, but you can forward the MMS to your Gmail. When you open the attachment in Gmail, it will import the contact.
They do actually work, I have had the same problem with my Nexus 5 & 6. I just have to randomly press the vCard icon repeatedly, fast presses, slow presses, holding it just until the message options pop up, closing Hangout and reopening, I haven't been able to work out which one it is though, but they will always work eventually. So it is not an unsupported issue, it is a bug on opening them issue.
You just need to touch the vCard green icon. A new window "view content card" opens, and there you have all the information at the pulldown arrow. The option "add to people" is also available on the top of the window.
