My animation consists of 250 frames and 6 layers. When I came back to my laptop this morning, I saw it only saves 250 frames, and they're all from the same layer. What did I do wrong, or where did it save my other rendered layers?
You need to change your ouput format to OpenEXR multilayer. After that you can access the different layers by adding an image node and changing the renderlayer like shown below.
If you want to use the sequence in an external compositor like nuke this should not be a problem. the channels are named according to the renderlayers (e.g renderlayer001.z).