We will review the beginning of experimental and theoretical

studies of moire systems and their evolution up to present. This type of

systems represent a new way of “growing” materials, and has tremendous

potential both for fundamental physics as well as for applications. Two

dimensional periodic crystals, whose separation between atoms is of order

angstroms, can be twisted controllably with respect to each other such

that they form new “periodicities”, called moire periodicities. In the new

“unit cell” we find thousands of atoms of the original crystal. These atoms

behave in ways that are incredibly counterintuitive. We show how the

controlled twisting of graphene and MoTe2 layers has led to a slew of

states of matter not possible in bulk conventional materials. We will show

how the collective behavior of thousands of p orbitals in a moire unit cell

of graphene can create single Heavy fermion at moire scale, and how the

interaction between such fermions can lead to a perfect quantum

simulator of an Anderson model. We will then present a catalogue of

possible twistable materials and show how a huge variety of strongly

interacting models can be realized in twisted homo and hetero twisted

bilayers and multilayers of these materials.