  This paper presents the general Schmidt decomposition of two-photon fields
generated in spontaneous parametric down-conversion (SPDC). It discusses in
particular the separation of the radial and azimuthal degrees of freedom, the
role of projection in modal analysis, and the benefits of collinear phase
mismatch. The paper is written in a review style and presents a wealth of
numerical results. It aims at emphasising the physics beyond the mathematics,
through discussions and graphical representations of key results.
