The temporal, spectral, and angular characteristics of the x-ray emissions (photons with energies within 5–1000 keV) are exhaustively investigated during the discharge formation at voltages up to 1 MV in approximately 55 cm air gaps. The temporal correlations between the x-ray emissions and discharge voltage and current waveforms are established. The evolution of the discharge plasma structures developing in the time periods of the x-ray generation is traced with a nanosecond resolution. Based on statistical data, theoretical analysis, and estimates the regularities in the x-ray emission characteristics are revealed together with their relationship with the ionization processes occurring in the gas-discharge medium. On the basis of the obtained experimental data, the probable x-ray generation mechanisms are discussed. The findings can provide a deeper understanding of the physics behind the sources of hard x rays arising during the development of laboratory and atmospheric discharges.