Explore the intricacies of seismic inverse problems in this 57-minute conference talk presented at SIAM GS15 by the Society for Industrial and Applied Mathematics. Delve into the world of seismic exploration, starting with a fisherman analogy to explain complex concepts. Learn about wave propagation, linear components, and offset in complex geometries. Discover modern methods like Full Waveform Inversion (FWI) and understand the loop skipping problem and the role of diving waves. Examine field records, results, and the pros and cons of various techniques. Investigate Wave Bath Tomography, survey sinking, velocity models, and the Extended Born Operator. Analyze offset and angle gathers, sensitivity kernels, and the importance of starting models. Conclude with real data applications and gain valuable insights into the future of seismic inverse problem solving.