MOTIVATION: Gene clustering and sample clustering are commonly used to find patterns in gene expression datasets. However, genes may cluster differently in heterogeneous samples (e.g. different tissues or disease states), whilst traditional methods assume that clusters are consistent across samples. Biclustering algorithms aim to solve this issue by performing sample clustering and gene clustering simultaneously. Existing reviews of biclustering algorithms have yet to include a number of more recent algorithms and have based comparisons on simplistic simulated datasets without specific evaluation of biclusters in real datasets, using less robust metrics. RESULTS: We compared four classes of sparse biclustering algorithms on a range of simulated and real datasets. All algorithms generally struggled on simulated datasets with a large number of genes or implanted biclusters. We found that Bayesian algorithms with strict sparsity constraints had high accuracy on the simulated datasets and did not require any post-processing, but were considerably slower than other algorithm classes. We found that non-negative matrix factorisation algorithms performed poorly, but could be re-purposed for biclustering through a sparsity-inducing post-processing procedure we introduce; one such algorithm was one of the most highly ranked on real datasets. In a multi-tissue knockout mouse RNA-seq dataset, the algorithms rarely returned clusters containing samples from multiple different tissues, whilst such clusters were identified in a human dataset of more closely related cell types (sorted blood cell subsets). This highlights the need for further thought in the design and analysis of multi-tissue studies to avoid differences between tissues dominating the analysis. AVAILABILITY: Code to run the analysis is available at https://github.com/nichollskc/biclust_comp, including wrappers for each algorithm, implementations of evaluation metrics, and code to simulate datasets and perform pre- and post-processing. The full tables of results are available at https://doi.org/10.5281/zenodo.4581206.