The goal of this thesis is to provide a modern interpretation and an extension of the classical
works of the 1970s and 1980s constructing moduli spaces of vector bundles and coherent sheaves
on projective spaces by means of "linear data", that is spaces of matrices modulo a linear group
action. These works culminated with the description by DreĢzet and Le Potier of the moduli spaces
of Gieseker-semistable sheaves on P2 as what are called today quiver moduli spaces. We show
that this can be naturally understood and generalized using the language of derived categories and
stability structures on them. In particular, we obtain analogous explicit constructions for moduli
of sheaves on P1xP1, and we investigate these moduli spaces using the theory of quiver moduli.
