Cellular biomechanics and cellular communication via receptor-ligand interactions play an important role in controlling cell development and maintaining cellular functions. Atomic force spectroscopy (AFM) technique has been widely used to characterize the changes in cellular biomechanics and quantify the receptor-ligand interactions. In this dissertation, we introduce working principles of AFM-based force spectroscopy, visualize cross-communications between membrane mechanics and cellular signaling, and identify quantitative relationship between receptor-ligand binding dynamics and multivalent interactions. First, by exploiting force spectroscopy methods, we probed biomechanical kinetics (stiffness, morphology, roughness, adhesion) of the brain, breast, prostate, and pancreatic cancer cells with standard chemotherapeutic drugs in normoxia and hypoxia over 12 – 24 hours. After exposure to the drugs, we found that brain, breast, and pancreatic cancer cells became approximately 20 – 50% less stiff, while prostate cancer cells became more stiff, due to either drug-induced disruption or reinforcement of cytoskeletal structure. However, the rate of the stiffness change decreased up to 2-folds in hypoxia, suggesting a correlation between cellular stiffness and drug resistance of cancer cells in hypoxic tumor microenvironment. Our results show that a degree of chemotherapeutic drug effects on biomechanical and biophysical properties of cancer cells is distinguishable in normoxia and hypoxia, which are correlated with alteration of cytoskeletal structure and integrity during a drug-induced apoptotic process. Second, we probed the binding strength of ligand-receptor interactions on live pancreatic cancer cells using single-molecule force spectroscopy methods, in which the peptides (cyclic arginine-glycine-aspartic acid: cRGD) was functionalized on a force probe tip through the polyethylene glycol-based bifunctional linker molecules. Although the density of integrin heterodimer receptors on the cell surface of each cell differs from cell to cell, the individual cRGD-integrin complexes exhibited a cell type-independent, monovalent bond strength. The load-dependent, bond strength of multivalent cRGD-integrin interactions scaled sublinearly with increasing bond number, consistent with the noncooperative, parallel bond model. Comparison of energy landscapes of the bond number revealed a substantial decrease of kinetic off rates for multivalent bonds, along with the widened width of the potential well and the increased potential barrier height between bound and unbound state, enhancing the stability of multivalent bonds between them.