Do review celebrities, whether it be for publications or YouTube channels, get to keep the items? Or do they have to buy them? I’ve always wondered.
"Celebrities" is a generous term, lol.
It depends on the price of the item, the level of the influencer, and the contract specifics honestly. When I was at one of the big audio companies we had a few options. For entry level products (usually $100-300ish) we would simply send X number of units out. Often times without contracts or guaranteed review. Usually the prompt was "use them, enjoy them, let us know what you think. And if you like, them, we'd love it if you posted a review and tagged XYZ and use hashtag XYZ."
For higher up mid-range stuff, we'd usually only send that to people we had signed deals with us. Usually if you provide a review of a certain length and/or use the product label out in X number of videos, you can keep it. This was very common for mid-range YouTubers.
We would also have some gear that were "review units" - this is the most common in the hifi world. Basically the manufacturer, or more commonly the distributor, will invest in an extra set of units they want sent around. Then they line up a "tour" of the products. Each review knows the window of time they should expect to have the unit, and about how long they should keep it. Once their time is up, the program manager tells them where to send the units next. These ultimately are offered to a reviewer at cost or later sold as open box. Sometimes these are also the pieces that get used at tradeshows.
But there are not hard and fast rules to these things. Like Hifi said, often times the review is a one off and the reviewer is offer the units at wholesale or sometimes even dealer price. Dealer price is usually a pretty good deal for the distributor because they basically get a quality review for the price of shipping and they know the unit is now in the reviewer's "stable" as a reference unit. But also, a lot of these reviewers are out there buying their own gear used and reselling it just to get on the map. For them, it's just part of the fun and if they can make back some of the money via YouTube views or ad revenue, that's all they need.
So quick answer - it's all over the place.