Random dynamical systems with bounded noise can have multiple stationary measures with different supports. Under variation of a parameter, such as the amplitude of the noise, bifurcations of these measures may occur. We discuss such bifurcations both in a context of random diffeomorphisms and of random differential equations. References: * A.J. Homburg, T. Young. Bifurcations for random differential equations with bounded noise on surfaces Topol. Methods Nonlinear Anal. 35 (2010), 77-98. * H. Zmarrou, A.J. Homburg. Dynamics and bifurcations of random circle diffeomorphisms Discrete Contin. Dyn. Syst. Ser. B 10 (2008), 719-731. * H. Zmarrou, A.J. Homburg. Bifurcations of stationary measures of random diffeomorphisms Ergod. Th. and Dynam. Sys. 27 (2007), 1651-1692.