  In the first part of this paper we construct a model structure for the
category of filtered cochain complexes of modules over some commutative ring
$R$ and explain how the classical Rees construction relates this to the usual
projective model structure over cochain complexes. The second part of the paper
is devoted to the study of derived moduli of sheaves: we give a new proof of
the representability of the derived stack of perfect complexes over a proper
scheme and then use the new model structure for filtered complexes to tackle
moduli of filtered derived modules. As an application, we construct derived
versions of Grassmannians and flag varieties.
