  We define a quasi--projective reduction of a complex algebraic variety $X$ to
be a regular map from $X$ to a quasi--projective variety that is universal with
respect to regular maps from $X$ to quasi--projective varieties. A toric
quasi--projective reduction is the analogous notion in the category of toric
varieties. For a given toric variety $X$ we first construct a toric
quasi--projective reduction. Then we show that $X$ has a quasi--projective
reduction if and only if its toric quasi--projective reduction is surjective.
We apply this result to characterize when the action of a subtorus on a
quasi--projective toric variety admits a categorical quotient in the category
of quasi--projective varieties.
