  This is the text accompanying my Bourbaki seminar on the work of Einsiedler
and Lindenstrauss on joinings. The first five sections surveys their proof of
the classification of joinings of higher-rank torus actions on arithmetic
quotients of semisimple or perfect algebraic groups. The last section surveys
how this classification can be used to tackle arithmetic problems, together
with a new application for higher rank simple groups.
