Blind channel estimation techniques were developed and usually evaluated for a given channel realization, i.e. with a deterministic channel model. On the other hand, in wireless communications the channel is typically modeled as Rayleigh fading, i.e. with a Gaussian (prior) distribution expressing variances of and correlations between channel coefficients. In this paper we explore a Bayesian approach to blind channel estimation, exploiting a priori information on fading channels. We mainly focus on joint ML/MAP estimation of channels and symbols on one hand, and on ML/MAP estimation of channels with elimination of symbols on the other hand. As a consequence, a unified framework in addition to three new Bayesian estimators are introduced where their performance is compared by simulations to three existing non-Bayesian estimators. In the same context, we provide an insightful discussion of the accurate way of deriving the Bayesian Cramer Rao bound (BCRB) with an emphasis on its singularity.