Global optimisation techniques and Molecular Dynamics simulations are employed to investigate the structure and the chemical order of AuCu clusters, with composition Au0.75Cu0.25, Au0.5Cu0.5 and Au0.25Cu0.75. Global optimisations by Parallel Excitable Walkers algorithm have located the global minimum configurations of clusters at size N = 100, 160 and 200 atoms. Stable clusters do not exhibit any alloy-like ordering, and combine the tendency to surface segregation of the gold atoms with the icosahedral structural motif. As unique exception to the icosahedral trend, an almost perfect decahedron is located at size N = 100, exhibiting copper atoms in its outer shell. As regards to the dynamics, the paper deals with the growth of AuCu clusters, both depositing gold and copper atoms onto an heterogeneous seed, and depositing copper atoms onto an homogeneous gold seed. In agreement with the global optimisation results, the former growth process leads to the formation of Ih clusters, whose surface is enriched in gold atoms. The latter deposition process turns into the formation of decahedral clusters with a reversed Cu(shell)Au(core) chemical ordering.