I will explain how to view the construction of moduli spaces of semistable sheaves on a projective variety as a functorial embedding into more basic projective varieties, namely moduli spaces of semistable Kronecker modules. This sheds new light on how to construct 'theta functions', i.e. natural projective coordinates on these moduli spaces. This is joint work with Alastair King (Invent. Math. 168 (2007) 613-666).