Conjugacy classes of derangements in finite transitive groups

Let $G$ be a permutation group acting transitively on a finite set $\Omega $. We classify all such $(G,\Omega )$ when $G$ contains a single conjugacy class of derangements. This was done under the assumption that $G$ acts primitively by Burness and Tong-Viet. It turns out that there are no imprimitive examples. We also discuss some results on the proportion of conjugacy classes which consist of derangements.