Fullerenes are spherical carbonaceous molecules with intriguing properties. On one side their corrugation resembles graphite or graphene, on the other side their curvature leads to a different behavior in many respects. For example, in contrast to flat graphite, a commensurate 1x1 phase exists for ethylene adsorbate molecules on curved C60. The adsorbate orientation, density, and binding strength (also referred to as adsorption, physisorption, or dissociation energy) depend strongly on the relation between the adsorbate-fullerene and the adsorbate-adsorbate interactions. The non-polar adsorbate molecules investigated in the present work wet the fullerenes, i.e. they cover the fullerenes layer by layer. Molecules with stronger inter-adsorbate interactions, such as water with its hydrogen bonds, prefer formation of drops that are bound as a cluster to the fullerene. A variety of new features arise for a substrate consisting of fullerene aggregates. The groove between two fullerenes enhances the adsorption energy almost by a factor of two, the dimple site between three fullerenes even more. Groove sites of arrays of carbon nanotubes are promising candidates for high-density energy storage in the form of hydrogen or methane. Fullerenes and their aggregates constitute a playground for studying adsorption properties both of carbonaceous surfaces and of molecular clusters. We performed computer simulations that accompanied mass spectrometric experiments on the same species. Our simulations guided understanding of anomalies in the experiments, so called magic numbers, and provided complementary microscopic information such as structures, energetics and phase transitions as functions of temperature.