we present recent results about finite jet determination of cr maps of positive codimension from real-analytic cr manifolds into real-algebraic subsets in complex space, or more generally nash subsets. one instance of such results is the unique jet determination of germs of cr maps from minimal real-analytic cr submanifolds in $\c^n$ into nash subsets in $\c^{n'}$ of d'angelo finite type, for arbitrary $n,n'\geq 2$. this is joint work with b. lamel.