Our current understanding of the evolution of obscured accretion onto supermassive black holes is reviewed. We consider the literature results on the relation between the fraction of moderately obscured, Compton-thin AGN and redshift, and discuss the biases which possibly affect the various measurements. Then, we discuss a number of methods - from ultradeep X-ray observations to the detection of high-ionization optical emission lines - to select the population of the most heavily obscured, Compton-thick AGN, whose cosmological evolution is basically unknown. The space density of heavily obscured AGN measured through different techniques is discussed and compared with the predictions by current synthesis models of the X-ray background. Preliminary results from the first half of the 3 Ms XMM observation of the Chandra Deep Field South (CDFS) are also presented. The prospects for population studies of heavily obscured AGN with future planned or proposed X-ray missions are finally discussed. Comment: 6 pages, 2 figures. Invited talk at the conference "X-ray Astronomy 2009: Present status, multiwavelength approach and future perspectives", September 2009, Bologna. To appear in AIP Conf. Proc. (editors: A. Comastri, M. Cappi, L. Angelini).