We summarise recent proposals for embedding the physics of cosmic strings and superstrings into
concrete models in string compactifications. Such embeddings feature epochs of moduli-mediated
matter domination which alter the resulting gravitational wave spectrum at frequencies that can be
computed from the properties of the network. Further, we study the effects of a varying tension,
which in string theory would be mediated by dynamical moduli. The resulting spectral index
is computed as a function of the equation of state of the background and the rate of variation
of the tension, showing that large spectral indices occur when the tension decreases. We then
study two scenarios: first, a simple scenario where the modulus decays gravitationally predicts a
feature in the LISA band when the PTA signal is used as a benchmark. Another scenario with
string-motivated potentials and moduli stabilisation provides a simple example of large boosts
in the spectrum at high frequencies. This work is a contribution to the proceedings of the third
general meeting of the COST Action CA21106 (Cosmic WISPers) and is based on [1, 2].