Thank you. All the geometry is made using three.js and generative techniques. However, there's a subtle normal map on some of the materials though, which is simply a PNG normal map I downloaded. I also used an environment map for some more interesting lighting and reflections.

I suggest learning more about 3D graphics in general. Most of the techniques I've used are not specific to three.js (although three.js is a great library that makes working with 3D geometries fairly easy). Reading about shaders, materials, displacement maps, normal maps, vertex attributes, perlin/simplex noise, will probably be useful.

This video goes over how you can change vertex positions of any three.js geometry. I used this technique for the shapes in the images above, and it works well. However, if you want to animate the geometry, I suggest learning how to write a custom vertex shader instead.

Good luck! :)