  It is well known that every finite simple group has a generating pair.
Moreover, Guralnick and Kantor proved that every finite simple group has the
stronger property, known as $\frac{3}{2}$-generation, that every nontrivial
element is contained in a generating pair. Much more recently, this result has
been generalised in three different directions, which form the basis of this
survey article. First, we look at some stronger forms of
$\frac{3}{2}$-generation that the finite simple groups satisfy, which are
described in terms of spread and uniform domination. Next, we discuss the
recent classification of the finite $\frac{3}{2}$-generated groups. Finally, we
turn our attention to infinite groups, focusing on the recent discovery that
the finitely presented simple groups of Thompson are also
$\frac{3}{2}$-generated, as are many of their generalisations. Throughout the
article we pose open questions in this area, and we highlight connections with
other areas of group theory.
