  We review properties of affine special Kaehler structures focusing on
singularities of such structures in the simplest case of real dimension two. We
describe all possible isolated singularities and compute the monodromy of the
flat symplectic connection, which is a part of a special Kaehler structure,
near a singularity. Beside numerous local examples, we construct continuous
families of special Kaehler structures with isolated singularities on the
projective line.
