  Let $\varphi$ be a holomorphic self-map of a bounded homogeneous domain $D$
in $\mathbb{C}^n$. In this work, we show that the composition operator
$C_\varphi: f\mapsto f\circ \varphi$ is bounded on the Bloch space
$\mathcal{B}$ of the domain and provide estimates on its operator norm. We also
give a sufficient condition for $\varphi$ to induce an isometry on $\cal{B}$.
This condition allows us to construct non-trivial examples of isometric
composition operators in the case when $D$ has the unit disk as a factor. We
then obtain some necessary conditions for $C_\varphi$ to be an isometry on
$\cal{B}$ when $D$ is a Cartan classical domain. Finally, we give the complete
description of the spectrum of the isometric composition operators in the case
of the unit disk and for a wide class of symbols on the polydisk.
