  The Ly$\alpha$ forest provides one of the best means of mapping large-scale
structure at high redshift, including our tightest constraint on the
distance-redshift relation before cosmic noon. We describe how the large-scale
correlations in the Ly$\alpha$ forest can be understood as an expansion in
cumulants of the optical depth field, which itself can be related to the
density field by a bias expansion. This provides a direct connection between
the observable and the statistics of the matter fluctuations which can be
computed in a systematic manner. We discuss the way in which complex,
small-scale physics enters the predictions, the origin of the much-discussed
velocity bias and the `renormalization' of the large-scale bias coefficients.
Our calculations are within the context of perturbation theory, but we also
make contact with earlier work using the peak-background split. Using the
structure of the equations of motion we demonstrate, to all orders in
perturbation theory, that the large-scale flux power spectrum becomes the
linear spectrum times the square of a quadratic in the cosine of the angle to
the line of sight. Unlike the case of galaxies, both the isotropic and
anisotropic pieces receive contributions from small-scale physics.
