In chemical physics, the energy landscape (the energy as a function of the coordinates of all the atoms) of a system is often characterized to try to understand the beahviour of a system, be it a cluster, biomolecule, supercooled liquid, ... For example, the ability of proteins to find their native structure has been ascribed to the funnel-like topography of the energy landscape, which guides unfolded proteins down towards the functionally active state. In this talk I look at some of the fundamental properties of energy landscapes. Somewhat surprisingly, I have found that the network of connections between states on the landscape is "scale-free" and that the basins of attraction surrounding the minima on the landscape form a fractal Apollonian-like packing of configuration space.