  We study asymptotically harmonic manifolds of negative curvature, without any
cocompactness or homogeneity assumption. We show that asymptotic harmonicity
provides a lot of information on the asymptotic geometry of these spaces: in
particular, we determine the volume entropy, the spectrum and the relative
densities of visual and harmonic measures on the ideal boundary. Then, we prove
an asymptotic analogue of the classical mean value property of harmonic
manifolds, and we characterize asymptotically harmonic manifolds, among
Cartan-Hadamard spaces of strictly negative curvature, by the existence of an
asymptotic equivalent $\tau(u)\ex^{Er}$ for the volume-density of geodesic
spheres (with $\tau$ constant in case $DR_M$ is bounded). Finally, we show the
existence of a Margulis function, and explicitly compute it, for all
asymptotically harmonic manifolds.
