The realist interpretations of quantum theory, proposed by de Broglie and by Bohm, are re-examined and their differences, especially concerning many-particle systems and the relativistic regime, are explored. The impact of the recently proposed experiments of Vigier et al. and of Ghose et al. on the debate about the interpretation of quantum mechanics is discussed. An indication of how de Broglie and Bohm would account for these experimental results is given.