Single-cell transcriptomics is a transformative technology to explore heterogeneous cell populations such as T cells, one of the most potent weapons against cancer and viral infections. Recent advances in this technology and the computational tools developed in their wake provide unique opportunities to build reference atlases that can be used to systematically compare new single-cell RNA-seq (scRNA-seq) datasets derived from different models or therapeutic conditions. We have developed ProjecTILs (https://github.com/carmonalab/ProjecTILs), a novel computational tool to project new scRNA-seq data into a reference map of T cells, allowing their direct comparison in a stable, annotated system of coordinates. ProjecTILs enables the classification of query cells into curated, discrete states, but also over a continuous space of intermediate states. We illustrate the projection of several datasets from recent publications over two novel cross-study murine T cell reference atlases: the first describing tumor-infiltrating T lymphocytes (TILs), the second characterizing acute and chronic viral infection. ProjecTILs accurately predicted the effects of multiple perturbations, including the ablation of genes controlling T cell differentiation, such as Tox, Ptpn2, miR-155 and Regnase-1, and identified novel gene programs that were altered in these cells (such as a Lag3-Klrc1 inhibitory module), revealing mechanisms of action behind these immunotherapeutic targets and opening new opportunities for the identification of novel targets. By comparing multiple samples over the same reference map, and across alternative embeddings, our method allows exploring the effect of cellular perturbations (e.g. as the result of therapy or genetic engineering) in terms of transcriptional states and altered genetic programs. *