  We say that a family of $k$-subsets of an $n$-element set is intersecting if
any two of its sets intersect. In this paper we study properties and structure
of large intersecting families.
  We prove a conclusive version of Frankl's theorem on intersecting families
with bounded maximal degree. This theorem, along with its generalizations to
cross-intersecting families, strengthens the results obtained by Frankl, Frankl
and Tokushige, Kupavskii and Zakharov and others.
  We study the structure of large intersecting families, obtaining some very
general structural theorems which extend the results of Han and Kohayakawa, as
well as Kostochka and Mubayi.
  We also obtain an extension of some classic problems on intersecting families
introduced in the 70s. We extend an old result of Frankl, in which he
determined the size and structure of the largest intersecting family of
$k$-sets with covering number $3$ for $n>n_0(k)$. We obtain the same result for
$n>Ck$, where $C$ is an absolute constant. Finally, we obtain a similar
extension for the following problem of Erd\H os, Rothschild and Sz\'{e}meredi:
what is the largest intersecting family, in which no element is contained in
more than a $c$-proportion of the sets, for different values of $c$.
