In oil and gas prospection, reflection seismology is the key method for inferring the geology of the first 10 km of the earth subsurface. This method uses controlled sources positioned at the surface of the earth and multiple "experiments" are repeated at different locations. The resulting large data sets of the collected seismograms are then processed to create a representation of a volume of sides of 10’s to 100’s of kilometers. While early imaging methods were relying on various approximations of wave propagation, recent advances in computing are now allowing us to solve this problem as a parameter estimation problem. Due to its extreme computational cost, and to the existence of multiple solutions, this method has only recently emerged as a viable approach and is starting to revolutionize the field of seismic prospecting. This talk will describe the approach of full-wavefield inversion in more detail and present the complexity of the approach as the physical fidelity of the governing equations is increased. The presentation will also describe some of the computational challenges associated with the practical aspects of this method, and in particular, the feasibility of multi-parameter inversion. Co-authors: Huseyin Denli, Alex Kanevsky, Dimitar Trenev, and Laurent White