Since the most common hexagonal (honeycomb shaped) droplet cluster was observed for the first time in 2004, new types of types of levitating droplet clusters were discovered. In a chain droplet cluster, rotating droplets may be very close to each other but viscosity of the thin gas layer between the droplets prevents them from coalescing. There is a reversible structural transition from the ordered hexagonal cluster to the chain-like structure. A hierarchical cluster is built of small groups of droplets with interactions controlled by the electrostatic force are combined into larger structures controlled by aerodynamic forces. Droplet aggregates keep continuously restructuring The droplets permanently keep rearranging, so the phenomenon is similar to the "deterministic chaos" (the Lorenz attractor). In the absence of the surfactant suppressing the thermocapillary (TC) flow at the surface of the water layer, a ring-shaped cluster is formed. Small clusters may demonstrate 4-fold, 5-fold, and 7-fold symmetry which is absent from large drolet clusters and colloidal crystals. The symmetry properties of small cluster configurations are universal, i.e., they do not depend on the size of the droplets and details of the interactions between the droplets. It was hypothesized that the symmetries in small clusters may be related to the ADE classification or to the simply-laced Dynkin diagrams.