Two views, and which one you want depends on the question you are asking.
There is no single combined report of every award against every person, so knowing which of the two answers your question saves a lot of clicking.

Open their expanded profile and go to the Awards section.
It is a collapsible section with a count badge, so you can see how many awards someone holds without even opening it. Expand it and you get the list of awards on that profile, plus a Give an award button for granting another one on the spot.
This is the view to use in a one-to-one conversation, before a reference call, or when someone asks why they did or did not receive something.
Go to Recognition, click the award's card, and you land on its People view. It has two sub-tabs:
If nobody has earned it, the Awarded tab says so plainly rather than showing an empty grid, and the same is true of Eligible.
Two things worth knowing, on each row:
That distinction settles most "how did they get this?" questions in one glance. If an award you built as manual-only shows Auto entries, or a milestone award shows more Manual entries than you expected, that is worth investigating before you trust the numbers in a report.
From the same rows you can Revoke award on one person, or tick several and choose Revoke selected.
It is your shortlist. On a rule-based award, it shows who has met the criteria, along with:
You can also grant straight from here: Award now next to one name, or tick several and use Award selected.
Yes. There is a Search users box, and sorting by:
Progress high to low is the useful one on a large Eligible list, because it puts the people closest to the line at the top.
Use Recalculate on the People view. It re-runs the eligibility evaluation for everyone against the current data.
Three situations where you should reach for it rather than assume the list is wrong:
Their own awards appear on their Awards page, under the Awards by Organization tab, separate from the platform-wide Vome Achievements on the Awards by Vome tab.
Two of your settings change what is visible there. An award set to Admin-only does not appear to them at all, and a Visibility Policy can hide it from people who do not meet its conditions. If somebody says they cannot see an award you know they hold, check those two before anything else.
Whether they see a progress bar toward an award they have not yet earned depends on Show Progress to Users on that award. With it off, the badge simply appears one day.
Yes. Award notification emails are recorded in the Admin Emails mailbox, under the Award notifications tab. That is the place to confirm a notification actually went out, which is a different question from whether the award was granted.
For the settings behind all of this, see Custom Awards & Recognition on Vome and What types of awards can I build?