In this paper, we study the spectral and scattering theory on the Hamiltonians which govern one-body quantum systems in crossed constant electric and magnetic fields. As one of the spectral features of the Hamiltonians, we show the absence of bound states of theirs under some appropriate conditions on the potentials. Moreover, by using the limiting absorption principle for the Hamiltonians, we give a simplified proof of the asymptotic completeness in short-range scattering.