Tumor tissue is often physically abnormal, and relationships to the altered genomes, selection, and heterogeneity of cancer are all crucial for understanding and likely for therapy. Mechanical properties, transport processes with reaction-diffusion, and even thermal fluctuations at the molecular scale can all modulate tumor cells, the tumor microenvironment, and the host. This is the physical context for the many genetic and epi-genetic changes that are increasingly being mapped and mathematically modeled in various cancers. How such physical changes/processes are manifest at multiple scales and contribute to cancer growth are current questions to be addressed by the many biophysicists and mathematically talented theorists now measuring and predictively modeling cancer cells and tumor tissues. To push back the boundaries of physics impacting biology, it is essential that the development of new and improved methodologies continues -- with quantitation in real physical units of force, length, time, and concentration providing some of the hard data that modelers can use for concrete physical predictions in cancer. An intimate interplay of Physical Measurement and Predictive Mathematics is precisely how the physical sciences has made progress for decades. This new GRC on Physical Science of Cancer aims to play a crucial role by providing a forum for the presentation and discussion of novel concepts and approaches. The current challenges in the field that we seek to focus on in sessions range from topics in Migration-Invasion mechanisms and Genomic Instability to Mathematical physics-based modeling for novel clinical trials in Immuno-Oncology.