  In this paper we prove a compactness result for Ricci flows with bounded
scalar curvature and entropy. It states that given any sequence of such Ricci
flows, we can pass to a subsequence that converges to a metric space which is
smooth away from a set of codimension $\geq 4$. The result has two main
consequences: First, it implies that singularities in Ricci flows with bounded
scalar curvature have codimension $\geq 4$ and, second, it establishes a
general form of the Hamilton-Tian Conjecture, which is even true in the
Riemannian case.
  In the course of the proof, we will also establish the following results:
$L^{p < 4}$ curvature bounds, integral bounds on the curvature radius,
Gromov-Hausdorff closeness of time-slices, an $\varepsilon$-regularity theorem
for Ricci flows and an improved backwards pseudolocality theorem.
