When a moiré pattern is formed by overlaying 2D semimetals or semiconductors with a twist or a difference in lattice constant, low-energy electrons and long-wavelength excitonic collective models are accurately described by periodic Hamiltonians with lattice constants on the 10 nm scales.  2D electron systems of this type have become known as moiré materials, which act like artificial crystals in which the number of electrons per effective atom can be electrically varied by around 10 – effectively moving through the moiré material periodic table.  In recent years moiré materials have emerged as a powerful platform for fundamental physics studies of strongly correlated matter, especially strongly correlated topological matter.  I will discuss different strategies for deriving moiré material effective Hamiltonians, and review some of the rich physics that has been observed in this materials platform.