  This is an expanded version of the two papers "Interpolation of Varieties of
Minimal Degree" and "Interpolation Problems: Del Pezzo Surfaces." It is well
known that one can find a rational normal curve in $\mathbb P^n$ through $n+3$
general points. More recently, it was shown that one can always find nonspecial
curves through the expected number of general points and linear spaces. After
some expository material regarding scrolls, we consider the generalization of
this question to varieties of all dimensions and explain why smooth varieties
of minimal degree satisfy interpolation. We give twenty-two equivalent
formulations of interpolation. We also classify when Castelnuovo curves satisfy
weak interpolation. In the appendix, we prove that del Pezzo surfaces satisfy
weak interpolation. Our techniques for proving interpolation include
deformation theory, degeneration and specialization, and association.
