Lead-based ferroelectric materials are of significant technological importance for sensing and actuation due to their high piezoelectric performance (i.e. the ability to convert an electrical signal to mechanical displacement, and vice versa). Traditionally, bulk ceramic or single crystals materials have filled these roles; however, emerging technologies stand to benefit by incorporating thin films to achieve miniaturization while maintaining high efficiency and sensitivity. Currently, chemical systems that have been well characterized in bulk form (e.g. Pb(Mg[1/3]Nb[2/3])O3 -- xPbTiO3, or PMN-xPT) require further study to optimize both the chemistry and structure for deployment in thin film devices. Furthermore, the effect of internal electric fields is more significant at the length scales of thin films, resulting in self biases that require compensation to reveal their intrinsic dielectric response. To this end, the structure-property relations of epitaxial PMN-xPT films sputter deposited on a variety of substrates were investigated. Attention was paid to how the structure (i.e. strain state, crystal structure, domain configuration, and defects) gave rise to the ferroelectric, dielectric, and piezoelectric response. Three-dimensional visualization of the dielectric response as a simultaneous function of electric field and temperature revealed the true phase transition of the films, which was found to correspond to the strain state and defect concentration. A lead-buffered anneal process was implemented to enhance the ferroelectric and dielectric response of the films without altering their stoichiometry. It was discovered that PMN-xPT films could be domain-engineered to exhibit a mixed domain state through chemistry and substrate choice. Such films exhibited a monoclinic distortion similar to that of the bulk compositions near the morphotropic phase boundary. Finally, it was revealed that the piezoelectric response could be greatly enhanced by declamping the film from the substrate via a membrane fabrication technique. The membrane structures exhibited enhanced domain wall mobility, suggesting that domain wall motion is crucial for strong piezoelectric performance in PMN-xPT films. The findings can help guide strain- and domain-engineered relaxor ferroelectric thin films tailored for particular applications.