  We revisit the complexity$=$action proposal for charged black holes. We
investigate the complexity for a dyonic black hole, and we find the surprising
feature that the late-time growth is sensitive to the ratio between electric
and magnetic charges. In particular, the late-time growth rate vanishes when
the black hole carries only a magnetic charge. If the dyonic black hole is
perturbed by a light shock wave, a similar feature appears for the switchback
effect, e.g., it is absent for purely magnetic black holes. We then show how
the inclusion of a surface term to the action can put the electric and magnetic
charges on an equal footing, or more generally change the value of the
late-time growth rate. Next, we investigate how the causal structure influences
the late-time growth with and without the surface term for charged black holes
in a family of Einstein-Maxwell-Dilaton theories. Finally, we connect the
previous discussion to the complexity=action proposal for the two-dimensional
Jackiw-Teitelboim theory. Since the two-dimensional theory is obtained by a
dimensional reduction from Einstein-Maxwell theory in higher dimensions in a
near-extremal and near-horizon limit, the choices of parent action and parent
background solution determine the behaviour of holographic complexity in two
dimensions.
