  The transition to turbulence in plane Poiseuille flow (PPF) is connected with
the presence of exact coherent structures. In contrast to other shear flows,
PPF has a number of different coherent states that are relevant for the
transition. We here discuss the different states, compare the critical Reynolds
numbers and optimal wavelengths for their appearance, and explore the
differences between flows operating at constant mass flux or at constant
pressure drop. The Reynolds numbers quoted here are based on the mean flow
velocity and refer to constant mass flux, the ones for constant pressure drop
are always higher. The Tollmien-Schlichting waves bifurcate subcritically from
the laminar profile at $Re=5772$ and reach down to $Re=2609$ (at a different
optimal wave length). Their localized counter part bifurcates at the even lower
value $Re=2334$. Three dimensional exact solutions appear at much lower
Reynolds numbers. We describe one exact solutions that is spanwise localized
and has a critical Reynolds number of $316$. Comparison to plane Couette flow
suggests that this is likely the lowest Reynolds number for exact coherent
structures in PPF. Streamwise localized versions of this state require higher
Reynolds numbers, with the lowest bifurcation occurring near $Re=1018$.
