We present STARsolo, a comprehensive turnkey solution for quantifying gene expression in single-cell/nucleus RNA-seq data, built into RNA-seq aligner STAR. Using simulated data that closely resembles realistic scRNA-seq, we demonstrate that STARsolo is highly accurate and significantly outperforms pseudoalignment-to-transcriptome tools. STARsolo can replicate the results of, but is considerably faster than CellRanger, currently the most widely used tool for pre-processing scRNA-seq data. In addition to uniquely mapped reads, STARsolo takes account of multi-gene reads, necessary to detect certain classes of biologically important genes. It has a flexible cell barcode processing scheme, compatible with many established scRNA-seq protocols, and extendable to emerging technologies. STARsolo can quantify transcriptomic features beyond gene expression, which we illustrate by analyzing cell-type-specific alternative splicing in the Tabula Muris project.