  The synergy between experiment, theory, and simulations enables a microscopic
analysis of spin-glass dynamics in a magnetic field in the vicinity of and
below the spin-glass transition temperature $T_\mathrm{g}$. The spin-glass
correlation length, $\xi(t,t_\mathrm{w};T)$, is analysed both in experiments
and in simulations in terms of the waiting time $t_\mathrm{w}$ after the spin
glass has been cooled down to a stabilised measuring temperature
$T<T_\mathrm{g}$ and of the time $t$ after the magnetic field is changed. This
correlation length is extracted experimentally for a CuMn 6 at. % single
crystal, as well as for simulations on the Janus II special-purpose
supercomputer, the latter with time and length scales comparable to experiment.
The non-linear magnetic susceptibility is reported from experiment and
simulations, using $\xi(t,t_\mathrm{w};T)$ as the scaling variable. Previous
experiments are reanalysed, and disagreements about the nature of the Zeeman
energy are resolved. The growth of the spin-glass magnetisation in zero-field
magnetisation experiments, $M_\mathrm{ZFC}(t,t_\mathrm{w};T)$, is measured from
simulations, verifying the scaling relationships in the dynamical or
non-equilibrium regime. Our preliminary search for the de Almeida-Thouless line
in $D=3$ is discussed.
