Multiverses

On the Multiverse. There are a variety of multiverse models but the most common one is that developed by Hugh Everett III to explain the phenomenon of Wave-Particle Duality. It is also known as the Many Worlds Interpretation (MWI). According to Everett all possible alternate histories and futures are real so that the various outcomes are realized over the sum of the many worlds. We live in a world which displays one of those outcomes. Like the other three explanations for Wave-Particle Duality (Collapse, Pilot and Copenhagen) the mathematics checks out. 
Multiverse modelling occurs in other areas of Physics. Max Tegmark, arguably one of the most brilliant physicists alive today, posits a classification system that consists of four levels that can be used to describe Multiverses.

Level One – Multiverses produced by cosmic inflation that have same physical constants and laws as does our universe;
Level Two – Multiverses produced by Chaotic inflation that have different constants and laws and are produced by a bubble effect (Andre Linde calculated that there are 10^10^10,000,000 of these);
Level Three – MWI Interpretation described above
Level Four – Constructs within Tegmark’s own mathematical universe hypothesis (a Theory of Everything that sees physical reality as a mathematical structure).

Brian Greene has a different classification system that has nine types and looks at simulations, holographs, cyclic phenomena, Branes etc.