A fundamental understanding of structure-property relationships is imperative in the rational design of new materials for tailored applications. In this dissertation, structure-property relationships are exploited in layered oxides and their composite materials. Recent advances in characterization techniques have allowed for more in-depth investigations into both the atomic level structure and properties of these materials. This dissertation focuses on understanding the structure-property relationships in supported catalytic systems and ferroelectric materials to aid in the rational design of functional materials.In Chapter 2, a correlation between the enthalpy of nanoparticle adsorption to oxide supports and the subsequent growth of these nanoparticles as a function of temperature is investigated. When deposited onto layered niobium oxide and tantalum oxide supports, rhodium hydroxide nanoparticles remain small and evenly dispersed upon heating to 750 oC. Using isothermal titration calorimetry, the bonding enthalpy of rhodium hydroxide nanoparticles to oxide supports is quantified for the first time under the wet synthetic conditions of catalyst preparation. Rh(OH)3 is concluded to have a strong, covalent interaction with the early transition metal oxide supports, and the interfacial bonding is hypothesized to occur through Rh -- O -- Nb bonding. Chapter 3 extends the studies in Chapter 2 to include supported metal, metal oxide, and metal hydroxide nanoparticles in the cobalt, nickel and copper triads. The data confirms a strong correlation between the heats of interaction and stability of the supported nanoparticles. Both experimental data and density functional theory calculations demonstrate that the support and nanoparticle compositions impact the heat of interaction and that the qualitative periodic trends of the metal bonding interaction are independent of the metal oxidation state. A strong bond is shown computationally to arise from the formation of mixed d-states between an adsorbed metal atom and a metal atom in the support.A preliminary investigation into the synthesis and stability of catalytically relevant ligand-free metal nanoparticles is presented in Chapter 4. The nanoparticles are synthesized via base hydrolysis and reduction with methanol. When deposited onto a niobium oxide support, the nanoparticles are thermally stable at temperatures up to 900 oC. The mechanism of platinum nanoparticle formation is still largely unknown, and a synthesis of rhodium and iridium ligand-free nanoparticles is reported.In Chapter 5, the n = 2 Dion Jacobson family A'LaB2O7 (A': Rb, Cs; B: Nb, Ta) is reported as non-centrosymmetric and piezoelectric at room temperature for the first time. This non-centrosymmetry is predicted to arise from two nonpolar oxygen octahedral rotational modes condensing via the hybrid improper ferroelectricity mechanism. Rietveld refinement of synchrotron X-ray diffraction data is unable to confirm an acentric crystal structure as peak splitting is evident, revealing that multiple phases are likely present in these materials.Chapter 6 presents temperature-dependent synchrotron X-ray diffraction and neutron diffraction Rietveld refinement analysis of CsLaNb2O7 to investigate the crystal structure and mechanism of non-centrosymmetry. The crystal structure is found to be in the centrosymmetric P4/mmm phase at 600 K and above. From 550 K to 350 K, the space group is assigned to the non-centrosymmetric Amm2 phase, as SHG signal is steadily increasing over this temperature range. Unfortunately, the 300 K and below crystal structure(s) have yet to be solved. Currently, both single-phase and dual-phase models are being refined in the synchrotron X-ray and neutron diffraction data.