  We provide a homotopy theorist's point of view on $KK$- and $E$-theory for
$C^{*}$-algebras. We construct stable $\infty$-categories representing these
theories through a sequence of Dwyer-Kan localizations of the category of
$C^{*}$-algebras. Thereby we will reveal the homotopic theoretic meaning of
various classical construction from $C^{*}$-algebra theory, in particular of
Cuntz' $q$-construction. We will also discuss operator algebra $K$-theory in
this framework.
