Cellular forces exerted on the extracellular matrix (ECM) during adhesion and migration under physiological and pathological conditions regulate not only the overall cell morphology but also nuclear deformation. Nuclear deformation can alter gene expression, integrity of the nuclear envelope, nucleus-cytoskeletal connection, chromatin architecture, and, in some cases, DNA damage responses. Although nuclear deformation is caused by the transfer of forces from the ECM to the nucleus, the role of intracellular organelles in force transfer remains unclear and a challenging area of study. To elucidate nuclear mechanics, various factors such as appropriate biomaterial properties, processing route, cellular force measurement technique, and micromanipulation of nuclear forces must be understood. In the initial phase of this review, we focused on various engineered biomaterials (natural and synthetic extracellular matrices) and their manufacturing routes along with the properties required to mimic the tumor microenvironment. Furthermore, we discussed the principle of tools used to measure the cellular traction force generated during cell adhesion and migration, followed by recently developed techniques to gauge nuclear mechanics. In the last phase of this review, we outlined the principle of traction force microscopy (TFM), challenges in the remodeling of traction forces, microbead displacement tracking algorithm, data transformation from bead movement, and extension of 2-dimensional TFM to multiscale TFM.