  Let $G$ be a simple linear algebraic group over an algebraically closed field
$K$ of characteristic $p \geqslant 0$, let $H$ be a proper closed subgroup of
$G$ and let $V$ be a nontrivial finite dimensional irreducible rational
$KG$-module. We say that $(G,H,V)$ is an irreducible triple if $V$ is
irreducible as a $KH$-module. Determining these triples is a fundamental
problem in the representation theory of algebraic groups, which arises
naturally in the study of the subgroup structure of classical groups. In the
1980s, Seitz and Testerman extended earlier work of Dynkin on connected
subgroups in characteristic zero to all algebraically closed fields. In this
article we will survey recent advances towards a classification of irreducible
triples for all positive dimensional subgroups of simple algebraic groups.
