  An $n$-vertex graph $G$ is a $C$-expander if $|N(X)|\geq C|X|$ for every
$X\subseteq V(G)$ with $|X|< n/2C$ and there is an edge between every two
disjoint sets of at least $n/2C$ vertices. We show that there is some constant
$C>0$ for which every $C$-expander is Hamiltonian. In particular, this implies
the well known conjecture of Krivelevich and Sudakov from 2003 on Hamilton
cycles in $(n,d,\lambda)$-graphs. This completes a long line of research on the
Hamiltonicity of sparse graphs, and has many applications, including to the
Hamiltonicity of random Cayley graphs.
