Combinatorial materials synthesis methods and high-throughput evaluation techniques have been developed to accelerate the process of materials discovery and optimization and phase-diagram mapping. Analogous to integrated circuit chips, integrated materials chips containing thousands of discrete different compositions or continuous phase diagrams, often in the form of high-quality epitaxial thin films, can be fabricated and screened for interesting properties. Microspot x-ray method, various optical measurement techniques, and a novel evanescent microwave microscope have been used to characterize the structural, optical, magnetic, and electrical properties of samples on the materials chips, These techniques are routinely used to discover/optimize and map phase diagrams of ferroelectric, dielectric, optical, magnetic, and superconducting materials.