  In the 1980s Dr\'ezet and Le Potier realized moduli spaces of
Gieseker-semistable sheaves on $\mathbb{P}^2$ as what are now called quiver
moduli spaces. We discuss how this construction can be understood using
t-structures and exceptional collections on derived categories, and how it can
be extended to a similar result on $\mathbb{P}^1\times\mathbb{P}^1$.
