  Massive complex scalar fields can form bound states around Kerr black holes.
These bound states -- dubbed scalar clouds -- are generically non-zero and
finite on and outside the horizon; they decay exponentially at spatial
infinity, have a real frequency and are specified by a set of integer "quantum"
numbers (n,l,m). For a specific set of these numbers, the clouds are only
possible along a 1-dimensional subset of the 2-dimensional parameter space of
Kerr black holes, called an existence line. In this paper we make a thorough
investigation of the scalar clouds due to neutral (charged) scalar fields
around Kerr(-Newman) black holes. We present the location of the existence
lines for a variety of quantum numbers, their spatial representation and
compare analytic approximation formulas in the literature with our exact
numerical results, exhibiting a sometimes remarkable agreement.
