Let $\mathfrak{g}$ be an affine Kac--Moody algebra and $U_q'(\mathfrak{g})$ be the associated quantized affine algebra. Kirillov--Reshetikhin modules are finite dimensional $U_q'(\mathfrak{g})$-modules labeled by a node $r$ of the Dynkin diagram together with a nonnegative integer $s$. It is expected that each Kirillov--Reshetikhin module has a crystal basis. In this talk, we focus on type $E_6^{(1)}$ for which Chari has given the decomposition of Kirillov--Reshetikhin modules into classical highest-weight modules. We extend the classical crystals for these modules to give an explicit combinatorial realization of the Kirillov--Reshetikhin crystals when $r$ is a leaf node of the finite Dynkin diagram and $s$ is arbitrary. This realization is based on the technique of promotion that has been used for other types by Shimozono and Fourier, Okado, Schilling. This is joint work with Anne Schilling.