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We consider the problem of source coding with side information (SI) at the decoder only, when the joint distribution between the source and the SI is not perfectly known. Four parametric models for this joint distribution are considered, where uncertainty about the distribution is turned into uncertainty about the value of the parameters. More precisely, a prior distribution for the parameters may or may not be available. Moreover, the value of the parameters may either change at every symbol or remain constant for a while. This paper overviews the results on the performance of lossless source coding with SI at the decoder for the four models. The way LDPC-based encoding and decoding schemes should be designed to cope with model uncertainty is provided. Most of the proposed practical schemes perform close to the theoretical limits.