The phases and microstructures in rapidly solidified Al-Cu-Ru alloys were investigated in this study. A chemically and topologically disordered icosahedral (i) phase grows dendritically from the liquid as the primary solidification product over the entire compositional region studied. The as-solidified i-phase is metastable and transforms to crystalline products at ≈500°C. The i-phase was not found as a product of the exothermic transformation for any composition, indicating that it is not the low temperature stable phase in the Al-Cu-Ru system;A chemically and topologically ordered i-phase was found to be an equilibrium phase at temperatures above ≈670°C and exists over a compositional region of several atomic percent. Once formed, this phase was easily retained at lower temperatures because of kinetic limitations of the transformation to the low temperature crystalline phase;Crystalline phases which from diffraction results appear structurally similar to the i-phase were also found in the Al-Cu-Ru system. These "approximant" phases aid in the determination of the atomic structure of i-phases by having common structural units. A simple cubic structure (a = 12.38 A, Pm3) containing a bcc network of icosahedral clusters was discovered. Comparisons of this phase with the i-phase indicated that strong similarities exist between the two structures;A rhombohedral approximant phase was also found. It exists as a transition state between the low-temperature crystalline phase and the high-temperature i-phase. This approximant phase also contains local icosahedral symmetry. The strong presence of icosahedral clusters in approximant phases in the Al-Cu-Ru system points to the distinct possibility that the i-phase is a quasiperiodic packing of icosahedral clusters of atoms.