  According to electronic structure theory, bilayer graphene is expected to
have anomalous electronic properties when it has long-period moir\'e patterns
produced by small misalignments between its individual layer honeycomb
lattices. We have realized bilayer graphene moir\'e crystals with accurately
controlled twist angles smaller than 1 degree and studied their properties
using scanning probe microscopy and electron transport. We observe conductivity
minima at charge neutrality, satellite gaps that appear at anomalous carrier
densities for twist angles smaller than 1 degree, and tunneling
densities-of-states that are strongly dependent on carrier density. These
features are robust up to large transverse electric fields. In perpendicular
magnetic fields, we observe the emergence of a Hofstadter butterfly in the
energy spectrum, with four-fold degenerate Landau levels, and broken symmetry
quantum Hall states at filling factors 1, 2, 3. These observations demonstrate
that at small twist angles, the electronic properties of bilayer graphene
moir\'e crystals are strongly altered by electron-electron interactions.
