  We present a detailed study of local and non-local correlations in the
electronic structure of elemental transition metals carried out by means of the
Quasiparticle Self-consistent GW (QSGW ) and Dynamical Mean Field Theory
(DMFT). Recent high resolution ARPES and Haas-van Alphen data of two typical
transition metal systems (Fe and Ni) are used as case study. (i) We find that
the properties of Fe are very well described by QSGW. Agreement with cyclotron
and very clean ARPES measurements is excellent, provided that final-state
scattering is taken into account. This establishes the exceptional reliability
of QSGW also in metallic systems. (ii) Nonetheless QSGW alone is not able to
provide an adequate description of the Ni ARPES data due to strong local spin
fluctuations. We surmount this deficiency by combining nonlocal charge
fluctuations in QSGW with local spin fluctuations in DMFT (QSGW + 'Magnetic
DMFT'). (iii) Finally we show that the dynamics of the local fluctuations are
actually not crucial. The addition of an external static field can lead to
similarly good results if non-local correlations are included through QSGW.
