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Knowledge of diffusivity is a prerequisite for understanding many scientific and technological disciplines. In this paper, firstly major experimental methods, which are employed to provide various diffusivity data, are briefly described. Secondly, the fundamentals of various computational methods, including first-principles method, embedded atomic method/molecular dynamic simulation, semi-empirical approaches, and phenomenological DICTRA technique, are demonstrated. Diffusion models recently developed for order/disorder transitions and stoichiometric compounds are also briefly depicted. Thirdly, a newly established diffusivity database for liquid, fcc_A1, L1₂, bcc_A2, bcc_B2, and intermetallic phases in the multicomponent Al alloys is presented via a few case studies in binary, ternary and quaternary systems. And the integration of various computational techniques and experimental methods is highlighted. The reliability of this diffusivity database is validated by comparing the calculated and measured concentration profiles, diffusion paths, and Kirkendall shifts in various binary, ternary and quaternary diffusion couples. Next, the established diffusivity databases along with thermodynamic and other thermo-physical properties are utilized to simulate the microstructural evolution for Al alloys during solidification, interdiffusion and precipitation. A special discussion is presented on the phase-field simulation of interdiffusion microstructures in a series of Ni-Al diffusion couples composed of γ, γ', and β phases under the effects of both coherent strain and external compressive force. Future orientations in the establishment of next generation of diffusivity database are finally addressed.