The oldest shoe is the Adidas Boost. This is made from expanded TPU that my employer BASF makes. This is a light shoe at 300 grams, and it is touted as having excellent "energy return." Meaning that the sole elastically returns energy to the running. When you are in the shoe it feels like it has a better grip on the street. It is a light weight shoe so the foot protection is not that great.
This is the Brook Ghost 6. It is 345 g (for one shoe) and has high foot protection. It is my newest show, and it does a nice job.
Here you can see the bottom, and the "gel" in the sole.
This is the Brook Rivenna 4. It is stiffer than the Ghost with less protection, and it is heavier at 407g per shoe.