  A remarkable feature of the band structure of bilayer graphene at small twist
angle is the appearance of isolated bands near neutrality, whose bandwidth can
be reduced at certain magic angles (eg. $\theta\sim 1.05^\circ$). In this
regime, correlated insulating states and superconductivity have been
experimentally observed. A microscopic description of these phenomena requires
an understanding of universal aspects of the band structure, which we discuss
here. First, we point out the importance of emergent symmetries, such as valley
conservation, which are excellent symmetries in the limit of small twist angles
and dictate qualitative features of the band structure. These have sometimes
been overlooked when discussing commensurate approximants to the band
structure, which we also review here, and solidify their connection with the
continuum theory which incorporates all emergent symmetries. Finally, we
discuss obstructions to writing down tight-binding models of just the isolated
bands, and in particular a new symmetry based diagnostic of these obstructions,
as well as relations to band topology and strategies for resolving the
obstruction. Especially, we construct a four-band model where the two lower
isolated bands realize all identified Wannier obstructions of the single-valley
nearly flat bands of twisted bilayer graphene.
