  We discuss black hole spin measurements employing the relativistic iron line
profiles in the X-ray domain. We investigate the iron line band for two
representative sources -- MCG -6-30-15 (active galaxy) and GX 339-4 (X-ray
binary). We compare two models of the broad iron line, LAOR and KYRLINE. We
realise that the spin is currently determined entirely from the position of the
marginally stable orbit while the effect of the spin on the overall line shape
would be resolvable with higher resolution X-ray missions. We show that the
precision of the spin measurements depends on an unknown angular distribution
of the disc emission. We study how sensitive the spin determination is to the
assumptions about the intrinsic angular distribution of the emitted photons. We
find that the uncertainty of the directional emission distribution translates
to 20% uncertainty in the determination of the radius of marginally stable
orbit. We perform radiation transfer computations of an X-ray irradiated disc
atmosphere (NOAR code) to determine the directionality of outgoing X-rays in
the 2-10 keV energy band. Based on these computations, we find that from the
simple formulae for the directionality, the isotropic case reproduces the
simulated data with the best accuracy. The most frequently used limb-darkening
law favours higher values of spin and, in addition, a steeper radial emissivity
profile. Furthermore, we present a spectral analysis of an XMM-Newton
observation of a Seyfert 1.5 galaxy IRAS 05078+1626 being the first X-ray
spectroscopic study of this source. The lack of the significant relativistic
blurring of the reflection model component suggests the accretion disc to be
truncated at a farther radius.
