In terms of some recent work of the author and collaborators, this paper provides a selfcontained account for the study of stochastic generalized porous media and fastdiffusion equations. We start from the corresponding deterministic equations in PDEs to explain the framework of the study, then introduce, respectively, results on the existence and uniqueness of solutions, the Harnack inequality for the associated transition semigroups and applications, the L² solutions and Large deviation principles with small noise.