Contrary to what some consumers, amateur photographers and even die-hard techies might assume, instant photography has been around a lot longer than the digital camera and the iPhone. In fact, it’s been around for more than six decades, ever since the scientist, visionary and Polaroid co-founder Edwin H. Land introduced his first “Land Camera” way back in 1947.

But it wasn’t until 1972, when Polaroid unveiled a marvelous (in every sense of the word) device called the SX-70, that an instant camera fully captured the imagination and the attention of photography buffs, industrial design aficionados and pop culture commentators alike. Far from a mere consumer product, the SX-70 quickly became associated with, and in a very real sense helped to define, the early Seventies.

But beyond its overnight stardom, the camera also, to varying degrees, presaged the ways in which the world now consumes, manipulates and shares media. Instagram, the iPhone, the Flip, even YouTube and streaming video — most of the sudden and playful means by which we entertain and inform ourselves every day can, with a little digging, find a kernel of their genius in the beautiful, compact universe of the SX-70.

Editor at large for TIME and self-described gadget-nerd Harry McCracken put the camera’s significance in perspective in a tremendous piece on Land and the SX-70 in June 2011. Citing the writer and scientist Arthur C. Clarke’s “law” that advanced technology is, at its best, indistinguishable from magic, McCracken wrote that he could not think “of a greater gadget than the SX-70 Land Camera…. [T]he sheer magnitude of its ambition and innovation dwarfs the Walkman, iPod, and nearly every other consumer-electronics product you can name.”

Here, more than 40 years after the SX-70 was introduced, LIFE.com pays tribute to Land’s vision and his determination to, as he once put it, “provide an opportunity for creativity that other photography doesn’t allow.”

Also in the gallery are pictures made with the SX-70 by LIFE photographer Co Rentmeester, who experimented with the camera while shooting the cover story on Land for the October 27, 1972, issue of the magazine.

— Ben Cosgrove is the Editor of LIFE.com

LIFE magazine cover: Co Rentmeester