The Predator is the latest chapter in a franchise that dates back to 1987. The original Arnold Schwarzenegger action-horror film is still regarded as the best in the series, if not the only good entry in the series. Shane Black actually played a member of Schwarzenegger's team in that film, and so it's little surprise that the man who co-wrote and directed the new entry paid tribute to the original in his own way.
There are several callbacks to the original Predator in the brand new entry. In many ways, the entire structure of the new film is meant to echo the original, but beyond that, there are clear moments where The Predator wants to remind you of the original film. Here are some of the best.
The Spacecraft Opening
One of the interesting things the original Predator does is leave the characters in the dark about exactly what it is they are facing, while at the same time informing the audience right up front that the Predator is an alien. We see the spaceship do a flyby of Earth and drop the creature onto the surface. The Predator opens in much the same way, with a Predator spaceship traveling through space, although this time, it's under attack by another craft. It uses some cool technology to jump through space and escape, arriving, once again, on Earth.
Stringing Up Its Prey
The first victims of the Predator we see in the original movie are skinned and hung by their feet in the trees. The first victim of the Predator in the new movie gets dropped from the tree branches dead and is also hanging by his feet. He's not completely skinned, but the Predator is in a hurry here and clearly doesn't have time for that sort of thing. This isn't the only aspect of the way the hunter acts like the alien from the first film. It leaps between treetops in the same way the original creature did, as opposed to say, the ones in Predators who mostly stayed on the ground and used their dogs to hunt like they were chasing a fox.