The Missing Link, invented by Steven P. Hanson and Jeffrey D. Breslow in 1981 and distributed by Ideal, has since then inspired new designs like the Whip-it, the Babylon Tower, the Eni Puzzle or the Capuzle.
Comprised by four columns and fifteen tiles, with a gap on the white column, you solve it by rotating the top and bottom layers and sliding the tiles up or down. The middle layers don't rotate, which will going to difficult your strategy to connect the right links again. The one I have doesn't turn very smoothly, but I reckon it's because is a bit old and could use a bit of lubricant. Nevertheless, it's a wonderful brainteaser and one of the most recognizable puzzles from the 80's.
The difficulty is a little more challenging than the Whip-It, for the reason mentioned above and for having four layers of tiles instead of just three. The Babylon Tower is more closely related to it in terms of difficulty. It has six columns with six rows each, but you can rotate every layer, so it balances out.
There's a few different versions of the Missing Link with various sizes, like the Pocket Edition with three layers, the Masters Edition with five layers, the Key Chain and the custom made Super Missing Link with six layers.
It's hard to find the Missing Link in stores nowadays, but you can see them often for sale at eBay.