I was looking at some pictures of amber recently, and was trying to think about how you would make this in Cycles. So far, I can understand making a model of the rock shape, and then using a translucent shader for the orange color, but that’s about as far as I’ve gotten. How would you make those streaks, and waves that are actually happening inside the amber? I was thinking maybe a custom-painted material, though I can’t figure out how to make it show on the inside. Any thoughts?
To get true volumetric streaks - you’ll probably have to drive a texture through the volumetric absorption, volumetric scatter or a mixture of both.
I’d consider modelling some of the internal geometry, such as the bubbles and cracks. I tried (and pretty much failed) to do something similar with the glaze in this image http://anopheles-design.deviantart.com/art/Whales-516114451 ; one day I’ll have another go. 
Watch and read this: http://www.creativeshrimp.com/create-realistic-ice-lighting-book-02.html
Your material can be simpler depending on how clean you want your amber to be
There should be an addon that comes with Blender that can work to create the interior surfaces.
It will slice up the mesh in a volumetric voronoi pattern, overlap the sliced mesh with the regular amber mesh, delete the shell and some of the interior faces, and give it a bit of subsurf and displacement. Then for the amber mesh, apply a volumetric material.
I really think volumetrics is a very bad idea for this material. Volumetric works best (perhaps “best” should be in inverted commas, it’s never worked all that well for me too). The internal shapes of the amber aren’t diffuse and cloudy, which is what you’ll get with volumetrics (and even if they were, you’d probably be better off faking it with ray depth), they’re sharp and precise - the shapes are being caused by refraction as the light interacts with bubbles and fractures inside; it’s a surface effect, not a volume effect.
I had a go here - not perfect, things like the fresnel and stuff needs tweaking.
I can post the node setup and wire if you like.
Yeah that looks great anopheles. Can you post up the nodes? How did you create those little bubbles inside?
Not so, because Cycles also has a volume absorption node which just affects the color and brightness of the rays without cloudiness.
Notice that the colors in the reference pics. are very deep, something that calls for use of such a volume.
You might also consider referencing some of Reynante Martinez’s shaders from his Cycles material studies. The download of ice material node setup may be particularly useful if you want to learn how to create some internal fractures for a material like this amber.
Ace - show me a render using cyles volumetrics that doesn’t look like crap and I’ll believe you. I restate my case - volumetrics will give you an opaque, cloudy effect (and be ridiculously noisy to boot). The inclusions in the amber material are bubbles and cracks - what you’re seeing is surface effects on those inclusions, so the best way to get them is with surface shaders; glossy, diffuse and refraction. The solid material has a little cloudiness to it, but you get a much better and much more controllable effect using the ray length node to fake it.
Acolyte - Even more useful is Gleb’s blog post on Ice, which I think Reynante used heavily. http://www.creativeshrimp.com/create-realistic-ice-lighting-book-02.html
Bombman - I did a quick particle system using icospheres as a mesh object, converted to mesh and flipped the normals. And I’ll post the material setup when I get a chance.
So here’s a screencap of the mesh I used and the materials.
The core shader is a pair of glass shaders mixed with a Layer Weight input to give a fresnel effect at glancing angles. I found it was too dark and clear, so I added a translucency node using the raylength method for faking volume absorption (based on the method at blenderdiplom); thicker parts of the amber have more translucent “glow”.
I also tried to add a bit of patina to the surface, but since mix shaders made the material very dark, I added a very slight reflectivity using add nodes. Use this approach sparingly; adding shaders means the material could end up reflecting more light than is supposed to be falling on it, but since amber has that kind of glowing look it seemed appropriate. I reckon the surface patina needs more work, but for a demo material I didn’t care enough. 
The internal shaders are much simpler; I found that mixing a transparent shader with another glass shader using layer weight was the best way to pick out the detail without making it too dark. The bubbles used a darker transparent shader with a slightly darker color value (even small changes from fully transparent made them much darker). One of the larger inclusions has a lower saturation, which intrestingly made it a bunch darker.
The mesh itself is just a distorted cube; the large inclusions are uv spheres that have been flattened and distorted using propotional editing, and the bubbles are a cloud of icospheres generated by an emission sim. Also, all the internal geometry has it’s normals flipped to point inward, and I took care to make sure there was no overlap with the outside mesh. It was a quick and dirty model, I think it’d look a lot better if I took more time over shaping the internal geometry.
Oh, it could also probably be improved with bumpmapping and/or displacement modifiers, especially on the internal geometry, which would make it look a little less clean inside, since the real inclusions have much more complex shapes. On the surface, a little too, but used much more sparingly - the surface of amber usually has a more polished appearance.
I knocked this together. It has a particle system for the bubbles (icosphere with flipped normals) and a volumetric absorption shader for the internal colour variations.
I think this looks pretty good - certainly very close to some amber I have seen. It’s not cloudy or particularly noisy (100 samples with a render time of less than 2 minutes on 480 GTX GPU). The noise that is there seems to come more from the glass shader than the volumetric shader (I know I tried it both with and without)
I haven’t modelled any inclusions - but not all amber has them anyway. I could add a second particle system with some black flecks in it to simulate trapped detritus. This would make it even more authentic.
Okay, I’ll give you that, that’s a great effect. 
However, I think that is exactly what I was trying to express by saying cloudy - while it’s not opaque, the edges of the volumetric colour are diffuse and soft, like an ink drop dissolving in water. That is a good amber effect, but I’d point out that it doesn’t actually reflect the OP’s reference images, which have a more even clarity to the volume.
You just increase the brightness value of the absorption color along with decreasing the density (you can go pretty much to 1 without adverse effects).
Also, his HDR lighting is different (compared to the really bright lighting of the reference images), so some difference in lighting is expected.
To get the sharp colour transitions/inclusions as per the OPs images - i’d just map a plane with a colour map on it - and then mix between transparent and colour using an alpha map.
moony that looks really amazing! nodes?
