The full-waveform inversion (FWI) method relies on an effective numerical solution of the wave equation. The wave equation must be solved numerous times during an inversion run. In the past, to be able to use FWI in practice, it was necessary to assume that the earth's subsurface was a 2D acoustic medium. Recent increases in computational power have made it possible to include more real-world physics in the FWI method, such that the computational subsurface can mimic the real-world subsurface as closely as possible. Going from 2D to 3D is challenging, primarily due to the numerical methods involved in solving the wave equation. Including elastic effects is not straightforward due to the increase in possible models that can explain the data, more complicated wave phenomena involved in the wave propagation, as well as trade-off between the subsurface elastic parameters during the inversion. We discuss some of the challenges and solution strategies for using the FWI method in the time domain using a 3D elastic computational domain.