Cells from different tissues typically look quite different from each other even when cultured on plastic or glass slides under identical conditions. This leads us to formulate the hypothesis that cell shape is a function of the cytoskeletal properties of those cells, and begs the question as to what information changes in cell shape carry. This question becomes all the more interesting for cancer, since invasive cancer cells are reported to have altered mechanical properties compared to non-invasive cancer cells. Inspired by this reasoning we study shape characteristics of paired osteosarcoma cell lines, each consisting of a less metastatic parental line and a more metastatic line, derived from the former by in vivo selection. Statistical analysis shows that shape characteristics of the metastatic cell lines are partly overlapping but on average distinguishable from the parental line. Significantly the shape changes fall into two categories, with three paired cell lines displaying a more mesenchymal-like morphology, while the fourth displaying a change towards a more rounded morphology. A neural network algorithm could distinguish between samples of the less metastatic cells from the more metastatic cells with near perfect accuracy. Thus subtle changes in shape carry information about the genetic changes that lead to invasiveness and metastasis of osteosarcoma cancer cells. The next challenge is to link these changes in shape with changes in mechanical cytoskeletal parameters. I will briefly discuss ongoing experiments to infer these cellular mechanical properties by studying internal fluctuations of organelles.