Integrated photonics enables complicated optical processes to occur on the surface of a chip, dramatically reducing device footprint. By integrating materials with optical nonlinearities onto integrated photonic platforms, chip-sized devices can perform a wider range of applications, such as frequency mixing. However, material choice impacts fabrication processes and device performance, so simultaneous optimization of nonlinear efficiency, material loss, and ease of fabrication becomes difficult. In this work, we explore two different avenues to improve nonlinear integrated photonic performance beyond material limitations. One method is through exploring new photonic materials. We measured the properties of a relatively new photonic material, aluminum scandium nitride (AlScN). Its CMOS-compatibility and enhanced second-order optical nonlinearity could enable scalable production of efficient nonlinear on-chip devices. After characterizing its optical properties through free-space second harmonic generation measurements, we fabricated an AlScN-based integrated photonics platform, demonstrating its use in an integrated electro-optic phase shifter. Though its electro-optic response was smaller than expected, recent theoretical calculations as well as improvements in fabrication methods provide a path towards improved performance in AlScN-based photonics. Another method is using photonic design to compensate for undesirable material properties. As one example, many optical materials experience significant loss at longer wavelengths, making far infrared (FIR) and terahertz (THz) sources difficult to produce. We simulated difference frequency generation (DFG) of FIR/THz light in thin film lithium niobate (TFLN) waveguides. By adjusting the poling period to control the phase matching condition, we achieved surface emission DFG to encourage immediate emission of the FIR/THz light. In this way, we can efficiently generate long wavelengths while avoiding high material loss. We also considered methods to enable beam steering of the emitted light for more flexibility in applications. By exploring two avenues in overcoming material limitations, we can push the boundaries of efficiency and capability in current devices and move towards improved performance in nonlinear integrated photonics.