  This mini-review presents a simple and accessible summary on the fascinating
physics of quantum nanomagnets coupled to a nuclear spin bath. These chemically
synthesized systems are an ideal test ground for the theories of decoherence in
mesoscopic quantum degrees of freedom, when the coupling to the environment is
local and not small. We shall focus here on the most striking quantum
phenomenon that occurs in such nanomagnets, namely the tunneling of their giant
spin through a high anisotropy barrier. It will be shown that perturbative
treatments must be discarded, and replaced by a more sophisticated formalism
where the dynamics of the nanomagnet and the nuclei that couple to it are
treated together from the beginning. After a critical review of the theoretical
predictions and their experimental verification, we continue with a set of
experimental results that challenge our present understanding, and outline the
importance of filling also this last gap in the theory.
