Cancer is a complex disease – improved methods of characterization and treatment prediction will require multiple scale integrated characterization of molecular and spatial characterization of tissue at multiple spatial and temporal scales. I will describe computational challenges and current efforts in cancer multi-scale imaging and molecular characterization, survey work carried out by the multi-scale cancer research community. I will focus on approaches that leverage complementary digital microscopy, radiology and "omic” analyses. In these scenarios, the objective is to use a coordinated set of image analysis, feature extraction and machine learning methods to predict disease progression and to aid in targeting new therapies. Finally, I will survey promising future approaches to applying data science and computation to cancer research.