Abstract: In this chapter, I present an overview of waveform tomography, in the context of imaging of the Earth‘s whole mantle at the global scale. In this context, waveform tomography is defined utilising entire wide-band filtered records of the seismic wavefield, generated by natural earthquakes and observed at broadband receivers located at teleseismic distances. This is in contrast to imaging methodologies that first extract secondary observables, such as, most commonly, travel times of the most prominent energy arrivals (i.e. seismic phases), that can be easily identified and isolated in the records. Waveform tomography is a non-linear process that requires the ability to compute the predicted wavefield in a given three-dimensional Earth model and compare it to the observed wavefield. One of its main challenges, is the computational cost involved. I first review the history of methodological developments, specifically focusing on the global, whole mantle Earth imaging problem. I then discuss and contrast the two recent methodologies that have led to the development of the first three-dimensional elastic global shear velocity models that have been published to-date using numerical integration of the wave equation, specifically, using the spectral element method. I discuss how the forward problem is addressed, the data selection approaches, definitions of the misfit function, and computation of kernels for the inverse step of the imaging procedure, as well as the choice of the optimisation method. I also discuss model parametrisation, and, in particular, the important topic of how the strongly heterogeneous crust is modelled. In the final parts of this chapter, I discuss efforts towards resolving the difficult problem of model evaluation and present my views on promising directions and remaining challenges in this rapidly evolving field, aiming at further improving resolution of deep mantle elastic structure with the goal of informing our understanding of the dynamics of our planet.