  Van der Waals (vdW) heterostructures ---formed by stacking or growing
two-dimensional (2D) crystals on top of each other--- have emerged as a new
promising route to tailor and engineer the properties of 2D materials. Twisted
bilayer graphene (tBLG), a simple vdW structure where the interference between
two misaligned graphene lattices leads to the formation of a moir\'e pattern,
is a test bed to study the effects of the interaction and misalignment between
layers, key players for determining the electronic properties of these
stackings. In this chapter, we present in a pedagogical way the general theory
used to describe lattice mismatched and misaligned vdW structures. We apply it
to the study of tBLG in the limit of small rotations and see how the coupling
between the two layers leads both to an angle dependent renormalization of
graphene's Fermi velocity and appearance of low-energy van Hove singularities.
The optical response of this system is then addressed by computing the optical
conductivity and the dispersion relation of tBLG surface plasmon-polaritons.
