We study the typing properties of {\em closure conversion} for 
simply-typed and polymorphic \mbox{$\lambda$-calculi}.  Unlike most accounts
of closure conversion, which only treat the untyped $\lambda$-calculus, 
we translate well-typed source programs to well-typed target programs.  
This allows later compiler phases to take advantage of types for
representation analysis and tag-free garbage collection, and 
it facilitates correctness proofs.  Our account of closure conversion for 
the simply-typed language takes advantage of a simple 
model of objects by mapping closures to {\em existentials}.  Closure
conversion for the polymorphic language requires additional type machinery, 
namely {\em translucency} in the style of Harper and Lillibridge's module
calculus, to express the type of a closure.