This paper provides an overview of the rapidly growing field of research on the biomechanics and biophysics of cancer cells. It begins by discussing the biology of cancer cells and the role of actin microfilaments, intermediate filaments, and microtubules in influencing cell mechanics, locomotion, differentiation, and neoplastic transformation. The paper then reviews various quantitative mechanical and physical assays used to extract the elastic and viscoelastic deformability of cancer cells, and presents results on cell mechanics for different types of cancer. Case studies are presented to illustrate how chemically induced cytoskeletal changes, biomechanical responses, and signals from intracellular regions interact with the chemomechanical environment of the extracellular matrix and molecular tumorigenic signaling pathways to effect malignant transformations. The effects of cancer drugs and chemotherapy regimens on cytoskeletal architecture and cell mechanics are also discussed. The paper concludes by highlighting the potential of understanding cancer cell deformability and its interactions with the extracellular environment for significant advancements in disease diagnostics, prophylactics, therapeutics, and drug efficacy assays.This paper provides an overview of the rapidly growing field of research on the biomechanics and biophysics of cancer cells. It begins by discussing the biology of cancer cells and the role of actin microfilaments, intermediate filaments, and microtubules in influencing cell mechanics, locomotion, differentiation, and neoplastic transformation. The paper then reviews various quantitative mechanical and physical assays used to extract the elastic and viscoelastic deformability of cancer cells, and presents results on cell mechanics for different types of cancer. Case studies are presented to illustrate how chemically induced cytoskeletal changes, biomechanical responses, and signals from intracellular regions interact with the chemomechanical environment of the extracellular matrix and molecular tumorigenic signaling pathways to effect malignant transformations. The effects of cancer drugs and chemotherapy regimens on cytoskeletal architecture and cell mechanics are also discussed. The paper concludes by highlighting the potential of understanding cancer cell deformability and its interactions with the extracellular environment for significant advancements in disease diagnostics, prophylactics, therapeutics, and drug efficacy assays.