  The general relativity vacuum black holes (BHs) can be scalarised in models
where a scalar field non-minimally couples to the Gauss-Bonnet (GB) invariant.
Such GB scalarisation comes in two flavours, depending on the GB sign that
triggers the phenomenon. Hereafter these two cases are termed GB$^\pm$
scalarisation. For vacuum BHs, only GB$^+$ scalarisation is possible in the
static case, while GB$^-$ scalarisation is $spin$ induced. But for
electrovacuum BHs, GB$^-$ is also $charged$ induced. We discuss the GB$^-$
scalarisation of Reissner-Nordstr\"om and Kerr-Newman BHs, discussing zero
modes and constructing fully non-linear solutions. Some comparisons with GB$^+$
scalarisation are given. To assess the generality of the observed features, we
also briefly consider the GB$^\pm$ scalarisation of stringy dilatonic BHs and
coloured BHs which provide qualitative differences with respect to the
electrovacuum case.
