  We report on Koszul-Tate resolutions in Algebra, in Mathematical Physics, in
Cohomological Analysis of PDE-s, and in Homotopy Theory. Further, we define an
abstract Koszul-Tate resolution in the frame of $\mathcal{D}$-Geometry, i.e.,
geometry over differential operators. We prove Comparison Theorems for these
resolutions, thus providing a dictionary between the different fields.
Eventually, we show that all these resolutions are of the new
$\mathcal{D}$-geometric type.
