ABSTRACT: With the introduction of the AAA algorithm in 2018 (Nakatsukasa-Sete-T., SISC), the computation of rational approximations changed from a hard problem to an easy one. We've been exploring the implications of this transformation ever since. This talk will review the algorithm and then present about 15 demonstrations of applications in various areas including interpolation of missing data, analytic continuation, analysis of solutions of dynamical systems, Wiener-Hopf and Riemann-Hilbert problems, function extension, model order reduction, and Laplace, Stokes, and Helmholtz calculations. BIOGRAPHY: Nick Trefethen is Professor of Applied Mathematics in Residence at Harvard University; during 1997-2023 he was Professor of Numerical Analysis and head of the Numerical Analysis Group at the University of Oxford. He was educated at Harvard and Stanford and held positions at NYU, MIT, and Cornell in earlier years. He is a Fellow of the Royal Society, a member of the US National Academy of Engineering, and a foreign member of the Chinese Academy of Sciences, and served during 2011-2012 as President of SIAM. He has won many prizes including the Gold Medal of the Institute for Mathematics and its Applications, the Naylor Prize of the London Mathematical Society, and the Polya and von Neumann Prizes from SIAM.He holds honorary doctorates from the University of Fribourg and Stellenbosch University. As an author Trefethen is known for his books including Numerical Linear Algebra (1997), Spectral Methods in MATLAB (2000), Spectra and Pseudospectra (2005), Approximation Theory and Approximation Practice (2013/2019), Exploring ODEs (2018), and An Applied Mathematician's Apology (2022). He organized the SIAM 100-Dollar, 100-Digit Challenge in 2002 and is the inventor of Chebfun and co-inventor of the AAA algorithm for rational approximation.