Complex oxide materials, which exhibit a wide range of structures and functionalities such as superconductivities, magnetic and multiferroic properties, have driven considerable research in materials science and condensed matter physics over past decades. As one important variant of oxide materials, ferroelectric materials which possess an electrically-addressable polarization hold great promise for next-generation non-volatile, low-power nanoelectronics. Leveraging the polarization and the coupled dielectric, piezoelectric, and pyroelectric properties, ferroelectric materials have been integrated into the state-of-the-art devices such as memories, logics, sensors/actuators, etc. My work is focused on developing new routes to engineering ferroelectric domain structures for enhanced dielectric response and controllable polarization switching in ferroelectric thin films that allow for new functionalities in device applications. In particular, I studied the evolution of domain structures, dielectric, and ferroelectric properties in PbZr0.2Ti0.8O3 thin films via the control of film orientation. First, using a combination of Ginzburg-Landau-Devonshire thermodynamic model and epitaxial thin film growth and characterization, I probed the domain structure and dielectric susceptibility in (001)-, (101)-, and (111)-oriented PbZr0.2Ti0.8¬O3 ¬thin films. In this work, I observe that (111)-oriented films, in which the extrinsic contributions from domain wall motion are frozen out, exhibit enhanced dielectric permittivity due to the stationary domain wall contribution from high densities of 90° domain walls. After exploring the enhanced dielectric response in (111)-oriented films, I studied how the polarization switching proceeds in films with different orientations. Differences are demonstrated between (001)-/(101)- and (111)-oriented films, with the latter exhibiting complex, nanotwinned ferroelectric domain structures with high densities of 90° domain walls and considerably broadened switching characteristics. Molecular-dynamics simulations predict both 180° (for (001)-/(101)-oriented films) and 90° multi-step switching (for (111)-oriented films) and these processes are subsequently observed in stroboscopic piezoresponse force microscopy. These results have implications for our understanding of ferroelectric switching and offer opportunities to change domain reversal speed. Furthermore, I demonstrated multi-state polarization switching in (111)-oriented PbZr0.2Ti0.8O3 thin films, wherein the polarization can be deterministically written into a number of non-volatile and stable states in any order by varying the driving voltage. Such switching phenomena are driven by kinetic control over the volume fraction of two geometrically different domain structures generated by two distinct switching pathways: one direct, bi-polar-like switching process and another multi-step process with the formation of a thermodynamically-stable intermediate twinning structure. This work provides new insights into the control of ferroelectric switching and demonstrates a candidate material with multi-state functionality for memory devices and adaptive neuromorphic electronics. Last, I explored the scaling potential of ferroelectric thin films for low-voltage operation and low-power consumption. In this work, it is noted that (111)-oriented PbZr0.2Ti0.8O3 films exhibit a deviation from JKD scaling with a smaller scaling exponent for the evolution of coercive field in films of thickness ≲165 nm. A combination of detailed X-ray structural analysis and first-principles calculations suggest a transition from tetragonal to monoclinic symmetry in films of thickness ≲165 nm contributes to the deviation from the expected scaling as the monoclinic phase has a lower energy barrier for switching. In addition, the reduced tetragonality in (111)-oriented heterostructures also drives a reduction of the remanent polarization and, therefore, a reduction of the overall energy barrier to switching which further exacerbates the deviation from the expected scaling. This work demonstrates a route towards reducing coercive fields in ferroelectric thin films and provides a possible mechanism to understand the deviation from JKD scaling. Overall, my work presented in this dissertation provides new insights into understanding fundamental mechanisms of emergent dielectric and ferroelectric properties in ferroelectric films and demonstrates a new route to engineering domain structures for enhanced dielectric response and controllable polarization switching in ferroelectric thin films that allow for new functionalities in device applications.