  Varieties of Fano type are very well behaved with respect to MMP, and they
are known to be rationally connected. We study the relation between classes of
rationally connected varieties and varieties of Fano type. We give examples of
rationally connected varieties of dimension $\geqslant 3$ which are not
birationally equivalent to Fano type varieties, thereby answering the question
of Cascini and Gongyo.
