This thesis explores the device engineering aspects of van der Waals heterostructures, focusing on methods to enhance capacitive coupling and modify the original band structure through Coulomb interaction and moiré engineering. The ability to control and engineer material properties has enabled new discoveries and insights into underlying quantum phenomena. Van der Waals heterostructures, with their diverse materials and tunable device configurations, provide a unique platform for exploring new physics. A key advancement in these systems is the development of dual-gated heterostructures, which allow precise control of electric fields and doping levels. Using the gate-sample capacitance, this work investigates insulating materials such as bilayer graphene under an electric field, as well as monolayer and bilayer WTe₂ and MoTe₂/WSe₂ heterobilayers. In these systems, resistivity quantum oscillations are observed, which are linked to the oscillatory behavior of the graphite gate’s density of states. This capacitive coupling modulates the carrier density in the sample even when the electrochemical potential is held constant. These results offer a new mechanism for understanding quantum oscillations in 2D insulators and emphasize the role of gate–sample interactions in tuning material properties. Another focus of this work is moiré engineering, achieved by stacking two 2D materials with a small twist angle, which creates a moiré pattern and modifies the band structure. In twisted bilayer WSe₂, this allows tuning of the van Hove singularity (vHS) using electric and magnetic fields. By moving the vHS across the Fermi level, phase transitions can be induced, stabilizing correlated states such as Stoner ferromagnetism and Chern insulators. These phenomena are driven by the enhanced electron-electron interactions near the vHS. Furthermore, the thesis demonstrates electrostatic imprinting of a moiré potential from a bilayer onto a monolayer semiconductor. This remote imprinting approach creates flat bands and correlated insulating states, with tunability via gating of the moiré layer. This method enables the study of quantum Hall states and other exotic phases without requiring direct interlayer tunneling. Overall, this work highlights the potential of van der Waals heterostructures for engineering novel electronic states through capacitive coupling and moiré engineering. These techniques offer unprecedented control over band structure and electronic phases, paving the way for future discoveries in quantum materials and the development of tunable quantum devices.