When differentially expressed genes are detected from samples containing different types of cells, only a very coarse overview without any cell type-specific information is obtained. Although several computational methods have been published to estimate cell type-specific differentially expressed genes from bulk samples, their performance has not been evaluated outside the original publications. Here, we compare accuracies of nine of these methods, test their sensitivity to various factors often present in real studies and provide practical guidelines for end users about when reliable results can be expected and when not. Our results show that TOAST, CARseq, CellDMC and TCA are accurate methods with their own strengths and weaknesses. Notably, methods designed to detect cell type-specific differential methylation were comparable to those designed for gene expression, and both types outperformed methods originally designed for other tasks. The most important factors affecting the accuracy of the estimated cell type-specific differentially expressed genes are (i) abundance of the cell type (rare cell types are harder to analyze) and (ii) individual heterogeneity in the cell type-specific expression profiles (stable cell types are easier to analyze)