The rapidly advancing field of biopolymers and adhesive materials is transforming both biomedical engineering and industrial technology. This transformation lies in the dynamic interplay between an understanding of cellular behavior and development of the materials that emulate these dynamic interactions. This approach addresses critical biomedical needs like smart wound healing and high-performance sealants, while also expanding industrial applications in packaging, marine engineering, and advanced electronics. Traditional biopolymers like hyaluronic acid (HA) and GelMA (both are extracellular matrix (ECM) proteins) remain invaluable for applications in tissue engineering and drug delivery due to their biocompatibility and tunable properties. Central to this progress lies in understanding cellular mechanotransduction. In our recent research we investigated the role of upregulated HA in hepatocellular carcinoma (HCC). Results show that the HCC cells can organize their cytoskeleton and move effectively on ultra-soft HA substrates (300 Pa), much as they do on much stiffer ones prepared with polyacrylamide (PAA) substrate (>30 kPa), when provided with essential biochemical signals such as HA and integrin ligands. However, the traction force generated on HA substrate is much lower than the stiff PAA substrate. This demonstrates that chemical signals can compensate for mechanical tension in cytoskeletal signaling, a process dependent on polyphosphoinositide turnover and Akt pathway activation. Our research further explores the distinct response of normal hepatocytes and HCC cells to mechanical properties of biopolymers such as elasticity and viscoelasticity. Unlike normal cells, Huh7 HCC cells spread faster and wider on viscoelastic substrates and exhibit enhanced motility and protrusions. Our model suggests that the stress relaxation time scales of viscoelastic substrates regulate cellular dynamics, indicating differing binding-unbinding rates of adhesion proteins in HCC cells compared to normal hepatocytes. This difference might explain varying cell spreading and motility in metastatic tissues.