Full Idea
In the second half of the twentieth century there emerged the opinion that foundation is the heart of the way to do set theory.
Gist of Idea
In the modern view, foundation is the heart of the way to do set theory
Source
William D. Hart (The Evolution of Logic [2010], 3)
Book Reference
Hart,W.D.: 'The Evolution of Logic' [CUP 2010], p.79
A Reaction
It is foundation which is the central axiom of the iterative conception of sets, where each level of sets is built on previous levels, and they are all 'well-founded'.