We study correlations between the X-ray spectral index, the strength of Compton reflection, and X-ray and radio fluxes in accreting black holes (Seyferts and black hole binaries). We critically evaluate the evidence for the correlation of the X-ray spectral index with the strength of Compton reflection and consider in detail statistical and systematic effects that can affect it. We study patterns of spectral variability (in particular, pivoting of a power-law spectrum) corresponding to the X-ray index-flux correlation. We also consider implications of the form of observed X-ray spectra and their variability for interpretation of the correlation between the radio and X-ray fluxes. Finally, we discuss accretion geometries that can account for the correlations and their overall theoretical interpretations.