The study of free-space quantum communications requires tools from quantum information theory, optics and turbulence theory. Here we combine these tools to bound the ultimate rates for key (and entanglement) distribution through a free-space link, where the propagation of quantum systems is generally affected by diffraction, atmospheric extinction, turbulence, pointing errors, and background noise. Besides establishing ultimate limits, we also show that the composable secret-key rate achievable by a suitable, pilot-guided, coherent-state protocol is sufficiently close to these limits, therefore showing the suitability of free-space channels for high-rate quantum key distribution.