Over the last decades, co-clustering models have spawned a number of algorithms showing the advantages that co-clustering can have over clustering. This is especially true for sparse high-dimensional data such as document-word matrices, which are our focus here. This proposal uses Latent Block Models (LBMs), rigorous statistical models that offer a variety of benefits in terms of flexibility, parsimony, and effectiveness. LBMs have been proposed in relation to different data types. This paper aims to embed existing and new models in a unified framework, focusing on exponential family LBM (ELBM) and the classification maximum likelihood approach. We then extend these models to include sparse versions, known as SELBM, taking into account the sparsity of datasets. The matrix formulations that we propose lead to simplified algorithms capable of addressing various types of data effectively.