  The famous Erd\H{o}s-Rademacher problem asks for the smallest number of
$r$-cliques in a graph with the given number of vertices and edges. Despite
decades of active attempts, the asymptotic value of this extremal function for
all $r$ was determined only recently, by Reiher [Annals of Mathematics, 184
(2016) 683--707]. Here we describe the asymptotic structure of all almost
extremal graphs. This task for $r=3$ was previously accomplished by Pikhurko
and Razborov [Combinatorics, Probability and Computing, 26 (2017) 138--160].
