Cancer cell lines are frequently used as in vitro tumour models. Recent molecular profiles of hundreds of cell lines from The Cancer Cell Line Encyclopedia and thousands of tumour samples from the Cancer Genome Atlas now allow a systematic genomic comparison of cell lines and tumours. Here we analyse a panel of 47 ovarian cancer cell lines and identify those that have the highest genetic similarity to ovarian tumours. Our comparison of copy-number changes, mutations and mRNA expression profiles reveals pronounced differences in molecular profiles between commonly used ovarian cancer cell lines and high-grade serous ovarian cancer tumour samples. We identify several rarely used cell lines that more closely resemble cognate tumour profiles than commonly used cell lines, and we propose these lines as the most suitable models of ovarian cancer. Our results indicate that the gap between cell lines and tumours can be bridged by genomically informed choices of cell line models for all tumour types.