Before revision: We describe the substitutive structure of Jeandel-Rao aperiodic Wang tilings \Omega_0. We introduce twelve sets of Wang tiles \{\mathcal{T_{i}\}_{1\leq i\leq 12} together with their associated Wang shifts \{i\}_{1\leq i\leq 12}.
After revision: Jeandel and Rao proved that 11 is the size of the smallest set of Wang tiles \{\mathcal{T_{i}\}_{1\leq i\leq 12} together with their associated Wang shifts \{i\}_{1\leq i\leq 12}.