I am trying to target hardware, and I am seeing programmers pay close attention from to what algorithms and models are supported by the current GPUs and CPUs. I see Unreal uses many different unique models, but how do these compare to the major models, like Phong, Monte Carlo, etc, are Unreal models derived from parts of these, or completely unique? And in what ways are the Unreal lighting/shading models supported by current hardware like in the XBoxOne and PS4?
You can read about the shader models here: Shading Models | Unreal Engine Documentation
As far as the engine goes you can also change the settings to accommodate the shader model you want to use.
For instance, these are the shader models available in UE4.
SM5: DirectX 11, Open GL 4.3+, PS4 and XB1
SM4: DirectX 10, Open GL 3.3+
Mobile/HTML 5: OpenGL ES2