  We present a detailed study of the reduction to 4D of 5D supergravity
compactified on the S^1/Z_2 orbifold. For this purpose we develop and employ a
recently proposed N=1 conformal superfield description of the 5D supergravity
couplings to abelian vector and hypermultiplets. In particular, we obtain a
unique relation of the "radion" to chiral superfields as in global 5D SUSY and
we can embed the universal hypermultiplet into this formalism. In our approach,
it is transparent how the superconformal structure of the effective 4D actions
is inherited from the one of the original 5D supergravity. We consider both
ungauged and gauged 5D supergravities. This includes compactifications in
unwarped geometries, generalizations of the supersymmetric Randall-Sundrum (RS)
model as well as 5D heterotic M-theory. In the unwarped case, after obtaining
the effective Kaehler potentials and superpotentials, we demonstrate that the
tree-level 4D potentials have flat and/or tachyonic directions. One-loop
corrections to the Kaehler potential and gaugino condensation are presented as
suitable tools for moduli stabilization to be discussed in subsequent work.
Turning to the RS-like models, we obtain a master formula for the Kaehler
potential for an arbitrary number of vector and hyper moduli, which we evaluate
exactly for special cases. Finally, we formulate the superfield description of
5D heterotic M-theory and obtain its effective 4D description for the universal
(h^(1,1)=1) case, in the presence of an arbitrary number of bulk 5-branes. We
present, as a check of our expressions, time-dependent solutions of 4D
heterotic M-theory, which uplift to 5D solutions generalizing the ones recently
found in hep-th/0502077.
