  The paper is related to the author's talk at the Hayama Symposium in Complex
Analysis in December 2000. In section 1 we survey results on the Oka principle
for sections of holomorphic submersions over Stein manifolds. In section 2 we
apply these results to the lifting problem for holomorphic mappings from Stein
manifolds, and in section 3 we apply them to the problem of removability of
intersections of holomorphic maps from Stein manifolds with closed complex
subvarieties of the target space.
