Traditional RNA sequencing (RNA-seq) allows the detection of gene expression variations between two or more cell populations through differentially expressed gene (DEG) analysis. However, genes that contribute to cell-to-cell differences are not discoverable with RNA-seq because RNA-seq samples are obtained from a mixture of cells. Single-cell RNA-seq (scRNA-seq) allows the detection of gene expression in each cell. With scRNA-seq, highly variable gene (HVG) discovery allows the detection of genes that contribute strongly to cell-to-cell variation within a homogeneous cell population, such as a population of embryonic stem cells. This analysis is implemented in many software packages. In this study, we compare seven HVG methods from six software packages, including BASiCS, Brennecke, scLVM, scran, scVEGs and Seurat. Our results demonstrate that reproducibility in HVG analysis requires a larger sample size than DEG analysis. Discrepancies between methods and potential issues in these tools are discussed and recommendations are made.