Experimental data for the structural and phase transformations taking place in cast equiatomic AlCrFeCoNiCu alloy under slow cooling, melt quenching, and a number of thermal treatments are presented. Investigations are carried out by analytical transmission electron microscopy and scanning electron microscopy, energy-dispersive X-ray spectroscopy, X-ray structural analysis, and X-ray diffraction analysis with the involvement of 3D atom probe tomography data, and nanohardness and elasticity modulus measurements. It is found that the as-cast alloy having a dendritic microstructure decomposes with the separation of at least six nanodimensional phases with different morphologies, structures (of type A2, B2, L12), and chemical compositions. It is also found that a homogeneous ultrafine-grained B2 structure arises in the alloy obtained by melt quenching. This structure decomposes into nanodimensional mainly equiaxial bcc phases, atomically ordered phases (B2), and atomically disordered ones (A2), all being highlighted by subsequent annealing.