The class of beta-generated distributions (Commun. Stat. Theory Methods 31:497–512, 2002; TEST 13:1–43, 2004) has received a lot of attention in the last years. In this paper, three new classes of bivariate beta-generated distributions are proposed. These classes are constructed using three different definitions of bivariate distributions with classical beta marginals and different covariance structures. We work with the bivariate beta distributions proposed in (J. Educ. Stat. 7:271–294, 1982; Metrika 54:215–231, 2001; Stat. Probability Lett. 62:407–412, 2003) for the first proposal, in (Stat. Methods Appl. 18: 465–481, 2009) for the second proposal and (J. Multivariate Anal. 102:1194–1202, 2011) for the third one. In each of these three classes, the main properties are studied. Some specific bivariate beta-generated distributions are studied. Finally, some empirical applications with well-being data are presented.