Explore computational challenges in gravitational wave parameter estimation in this 45-minute lecture by John Veitch from the University of Glasgow's Physics and Astronomy department. Delve into the complexities of analyzing compact binary signals, examining traditional stochastic sampling methods used in recent O1-O3 runs and the need for improved efficiency. Discover novel deep learning techniques that significantly reduce latency, and consider their flexibility for non-standard analyses. Gain insights into future parameter estimation requirements and cutting-edge methods addressing these challenges. Cover topics including results from GWTC3 and GWTC4, computational details, sampling techniques, competitive light methods, benchmarks, reduced order modeling, nested sampling, normalization, contour sampling, speed limits, and more.