  We give an overview of the theory of framed correspondences in motivic
homotopy theory. Motivic spaces with framed transfers are the analogue in
motivic homotopy theory of $E_{\infty}$-spaces in classical homotopy theory,
and in particular they provide an algebraic description of infinite
$\mathbb{P}^1$-loop spaces. We will discuss the foundations of the theory
(following Voevodsky, Garkusha, Panin, Ananyevskiy, and Neshitov), some
applications such as the computations of the infinite loop spaces of the
motivic sphere and of algebraic cobordism (following Elmanto, Hoyois, Khan,
Sosnilo, and Yakerson), and some open problems.
