This article addresses the modeling of reverberant recording environments in the context of under-determined convolutive blind source separation. We model the contribution of each source to all mixture channels in the time-frequency domain as a zero-mean Gaussian random variable whose covari- ance encodes the spatial characteristics of the source. We then consider four specific covariance models, including a full-rank unconstrained model. We derive a family of iterative expectation- maximization (EM) algorithms to estimate the parameters of each model and propose suitable procedures adapted from the state- of-the-art to initialize the parameters and to align the order of the estimated sources across all frequency bins. Experimental results over reverberant synthetic mixtures and live recordings of speech data show the effectiveness of the proposed approach.