So, Robin #1. No, not the one that was released a week or so ago and had its speculation-fueled sell-out. I mean the now (urgh) 30+ year old mini-series that was absolutely red-hot. You know, this one:

I can still remember trying to smooth out the creases in the door-sized promo poster they sent out for this thing while trying to display it in the shop. But anyway, as I was saying, this was a big seller, and demand was so high it went into second and even third printings. And they way you can tell these printings? By the little Roman numerals in the corner box there:

…which, I guess, makes those reprintings variants, thus fitting into the topic at hand. I kind of preferred this to DC’s later practice of changing cover colors or images to identify new printings, frankly, though I can understand the logic behind it. What’s gonna convince someone to double or triple dip on a comic they already bought? A little “III” or a whole new design? [EDIT: pal Nat reminds me that the contemporaneous Killing Joke also used colors to distinguish printings.]
At any rate, this is really as close as the first Robin series came to having variant covers. But don’t worry, dear reader, as they made up for it with 1991’s Robin II series.
This four issue mini-series had a decreasing number of variants as the series went on, starting with five variants for the first issue (not counting the “newsstand variant” with the UPC code, because c’mon), then four for the second, three for the third, and two for the fourth. Got that? Good.
For each issue there was one cover that was “normal,” and then the variant(s) would each feature different cover images and a hologram slapped on there, thusly:

And look, here’s the hologram IN ACTION, as filmed-and-GIFfed by my own self:

Exciting, right? How could you not want a full set of all those variant covers for each issue? Well, hang onto to your little green shorts, friend, because DC’s got you covered (get it?):

Yes, DC also marketed complete sets of all variants issue-by-issue in this polybagged packages, Plus a hologram trading card!
If this seems…somewhat excessive, you’re not wrong. It’s like Robin II somehow managed to take the multiple covers of X-Men #1 and the polybagged editions of Spider-Man #1 and formed them into this unholy collectible amalgam. By the way, when DC says “newsstand,” they just mean the regular non-hologram cover (which was offered both in a UPC-less direct sales version and a UPC-ed version you’d find at 7-11 or whathaveyou.)
Now, as far as the variants themselves…while not the first comic to have a hologram affixed to the cover (that would be Boffo Laffs #1 from 1986, I believe), the holograms do feature nicely iconic images of Robin, Batman, the Joker, and the Bat-signal on each succeeding installment (and the same hologram appears on all the variants for that particular ish). They’re also usually well-incorporated into the covers, though I kinda wonder about this Matt Wagner one:

Is the Joker, like, thinking about Robin or something? Is that what that’s representing? Or did the asylum put up a framed hologram in his cell just to rub it in? Great drawing of the Joker, though.
Okay, in case DC wasn’t reaching into your pocket enough, they also had this $30 mega-collector’s slipcase set, for which I totally stole images from eBay auctions so I could illustrate it here:

And in case you didn’t have enough holographic technology from the comics themselves, get ready for this thing on the slipcase:

Now, it’s been a while since I handled one of these. I know at the previous place of employment we kind of had one kicking around the backroom for a while that I’d continually put on the eBays ’til it finally sold (I think). And the contents are…just what they say there on the label. I seem to remember the “two custom backing boards” being not really anything you’d want to use in your comic bags…kinda flimsy, and I’m pretty sure they had holographic stickers on those, too, because why not.
Speaking of holograms, since “hologram” was pretty much every other word in the last paragraph, if I recall correctly one of the promo items for this series was a little holographic sticker with Robin’s “R” printed on it. I can literally still see the small bundles of these we got from DC, unless of course I’m imagining these and they never existed. Which, you know, I wouldn’t put past my brain at this point.
So that series sells well, as you might have imagined, and you know what that means. That’s right, Robin III in 1993, which scaled back the variant-ism to just two covers per each issue of this six-issue run. You had your standard, regular, boring static image cover printed on regular paper that Grandma prefers, and then you had…SPECIAL MOTION COVERS:

Alas, I didn’t have any of these in the shop right right now, otherwise I would have made an awesome GIF of this too. But trust me, you pulled the little tab on that cover and you cold make that image change. And it was a two-sided thingie too, so you could pull that insert entirely out, flip it over, and have a brand new image moving back-and-forth on that cover. I’m pretty sure that’s what they mean by “reversible cover” on the polybag that each of these “special moving covers” came in:

The poster noted at the bottom, kinda obscured by the folding of the bag’s bottom, was a poster of the comic’s regular cover. I thought that was a good touch and a solid bonus for fans.
One of my favorite things about the Robin III mini-series was that a demonstration copy of the special cover was sent to retailers. It looked like just another copy of the comic, but the pages inside were all blank. Honestly, I wish publishers would offer “blank” versions of some of those more speculated comics coming out now…would save them some money and they’re just gonna end up unreadable in CGC slabs anyway so they might as well be blank. Anyway, we had a lot of fun showing that Advanced Cover Technology to the customers, and that certainly moved some copies for us.
Following that in 1993 was the first issue of the ongoing Robin series, which ran quite a while and, oh yes, had variant covers for the first issue. You had your standard flat cover, and then you had this embossed beauty:

…with the figure featuring raised “3-D” puffy bits so you could examine Robin’s contours with your fingertips to your heart’s content.
Now, that aftermarket for these is a little hard to judge personally, in that I have copies of the first mini, one or two of the second, and none of the third currently in stock. I know while that original Robin ongoing was, well, going, the back issue sales on the various minis were very strong…especially for that original #1. I know at the previous place of employment we had a couple of those Robin II polybagged bundles still kicking around, and I noted how hard it was for me to move that slipcased set. A look at eBay shows at least the slipcased books are doing well now, so I guess I was just a decade or so early in trying to list the thing.
In collections I’d take in at my own shop, the most common of the Robin #1s I’d find would be that embossed cover for the ongoing series. I suppose a lot of people wanted to feel their Robins.
What’s next? I don’t know! The thirteen Gen13 covers? The trend of retailer-exclusive “platinum” editions for certain Big Comics? Or something else entirely? If you have a preference, you know how to tell me!