Biopolymers have many unique properties which play an essential and pervasive role in everyday life, thus making them attractive for engineering applications. Understand- ing how the particular properties of biopolymers give rise to important applications in technology remains a long-standing challenge. Although biopolymers can have different chemistries, they share some common physical properties: high molecular weights, stiff backbones, and complex internal structures. Computer simulation, therefore, plays quite an important role since it provides a way to study a generic model that, by changing the parameters appearing in the model, permits studying a wide variety of biopolymers. Specifically, we focus on two such biopolymers: DNA and methylcellulose. This thesis focuses on studying the universal properties of the two aforementioned biopolymers using novel molecular simulation techniques. DNA attracts particularly strong interest not only because of its fascinating double- helix structure but also because DNA carries biological information. Genomic mapping is emerging as a new technology to provide information about large-scale genomic structural variations. In this context, the conformation and properties of the linearized DNA are only beginning to be understood. With a Monte Carlo chain growth method known as pruned-enriched Rosenbluth method, we explore the force-extension relationship of stretched DNA. In this scenario, external forces and confinement are two fundamental and complementary aspects. We begin by stretching a single DNA in free solution. This allows separation of restrictions imposed by forces from that by walls. This work shows that the thickness of DNA plays an important role in the force-extension behavior. The key outcome is a new expression that approximates the force-extension behavior with about 5% relative error for all range of forces. We then analyze slit-confined DNA stretched by an external force. This work predicted a new regime in the force-extension behavior that features a mixed effect of both sensible DNA volume and sensible wall effects. We anticipate such a complete description of the force-extension of DNA will prove useful for the design of new genomic mapping technologies. The dissertation also involves another biopolymer, methylcellulose, which has an extremely wide range of commercial uses. Methylcellulose is thermoresponsive polymer that undergoes a morphological transition at elevated temperature, forming uniform diameter fibrils. However, mechanisms behind the solution-gel transition are poorly understood. Following the computational studies by Huang et al. , we apply Langevin dynamics simulations to a coarse-grained model that produces collapsed ring-like structures in dilute solution with a radius close to the fibrils observed in experiments. We show that the competition between the dihedral potential and self-attraction causes these collapsed states to undergo a rapid conformational change, which helps the chain to avoid kinetic traps by permitting a transition between collapsed states. We expect our findings from computational studies of biopolymers will not only provide a deep understanding of semiflexible polymer physics but also inspire novel engineering applications relying on the properties of biopolymers.