This talk is concerned with bifurcation of random dynamical systems generated by non-autonomous stochastic equations. We first introduce definitions of pathwise random almost periodic and almost automorphic solutions for stochastic equations, which are corresponding counterparts of non-autonomous deterministic systems. We then discuss pitchfork bifurcation of random periodic (almost periodic, almost automorphic) solutions of equations with multiplicative noise. We also demonstrate that additive white noise could destroy bifurcation of non-autonomous deterministic equations. Finally, we discuss bifurcation of random periodic solutions of a class of stochastic parabolic equations on bounded domains.