  The five exceptional simple Lie algebras over the complex number are included
one within the other as $G_2 \subset F_4 \subset E_6 \subset E_7 \subset E_8$.
The biggest one, $E_8$, is in many ways the most mysterious. This article
surveys what is known about it including many recent results, focusing on the
point of view of Lie algebras and algebraic groups over fields.
