There are records of other realms existing in our world. The are not the same as alternate dimensions.
Generally considered to be the "normal" world. All alternate dimensions contain an Overworld of some form, almost as an anchor point. Each version of the Overworld has it's own version of other realms. For unknown reasons some worlds can access certain other realms, and some can not. It is most common for worlds to have access to the Nether and End realms.
Accessible Realms Edit
A fiery realm, considered by some to be close to the core of the planet, filled with lava and hostile fiery creatures. The Nether is accessible via obsidian portals, a magical construct. Some attempts have been made at investigating this realm by the state.
The End Edit
A crumbling and empty land, home to the Endermen and domain of the Enderdragon. It is speculated this realm has a closer link to the void than the standard Overworld, but the hostility and bareness of this realm makes studies impossible. Enderportals can rarely be found buried underground in ancient strongholds. They're magical in nature, but where they originate from in unknown.
The Dream World Edit
A strange realm accessible by magical means when sleeping. Depending on the luck of the traveller entering it, the dream world can be either pleasant and ethereal, or a "nightmare" filled with aggressive creatures. Only specific items can be brought in and out of the Dream World. One cannot die in this realm, as taking damage simply awakens the dreamer.
Inaccessible/Other Realms Edit
The Aether Edit
The realm from which Blue originates. There are no records of this realm in the current world. Blue fell from the Aether when she was young and thus can not personally remember being there, but learned all she could about it in her home world, which possessed records of that realm.