  Small-twist-angle bilayer graphene supports strongly correlated insulating
states and superconductivity. Twisted few-layer graphene systems are likely to
open up new directions for strong correlation physics in moir\'e superlattices.
We derive and study moir\'e band models that describe the electronic structure
of graphene trilayers in which one of the three layers is twisted by a small
angle relative to perfect AAA, ABA, or ABC stacking arrangements. We find that
the electronic structure depends very strongly on the starting stackings
arrangement and on which layer is twisted. We identify ABA stacking with a
middle-layer twist as a promising system for itinerant electron magnetism or
even more robust superconductivity, because it exhibits both large and small
velocity bands at energies near the Fermi level.
