  In this text we review various relations between building blocks of closed
and open string amplitudes at tree-level and genus one. We explain that KLT
relations between tree-level closed and open string amplitudes follow from the
holomorphic factorisation of conformal correlation functions on conformal
blocks. We give a simple hands-on evaluation of the $\alpha'$-expansion of
tree-level closed string amplitudes displaying the special single-valued nature
of the coefficients. We show that the same techniques can be used also at
genus-one, where we give a new proof of the single-valued nature of the
coefficients of 2-point closed string amplitudes. We conclude by giving an
overview of some open problems.
