The recent upswing of microfluidics and combinatorial indexing strategies, further enhanced by very low sequencing costs, have turned single cell sequencing into an empowering technology; analyzing thousands—or even millions—of cells per experimental run is becoming a routine assignment in laboratories worldwide. As a consequence, we are witnessing a data revolution in single cell biology. Although some issues are similar in spirit to those experienced in bulk sequencing, many of the emerging data science problems are unique to single cell analysis; together, they give rise to the new realm of ‘Single Cell Data Science’. Here, we outline twelve challenges that will be central in bringing this new field forward. For each challenge, the current state of the art in terms of prior work is reviewed, and open problems are formulated, with an emphasis on the research goals that motivate them. This compendium is meant to serve as a guideline for established researchers, newcomers and students alike, highlighting interesting and rewarding problems in ‘Single Cell Data Science’ for the coming years.