We discuss the structure of Heterotic/Type II duality in four dimensio
ns as a consequence of string-string duality in six dimensions. We emp
hasize the new features in four dimensions which go beyond the six dim
ensional vacuum structure and pertain to the way particular K3 fibers
can be embedded in Calabi-Yau threefolds. Our focus is on hypersurface
s as well as complete intersections of codimension two which are conne
cted via conifold transitions.