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.
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