Seismic tomography is an ill-posed inverse problem due to the irregular distribution of earthquakes and seismic stations. The solution is hence not unique and regularization is required which makes error analyses arbitrary. We adopt a different approach, based on Monte Carlo sampling, which finds all models compatible with the data. We transform the solutions thus found into probability density functions (pdfs) for the parameters of interest. In the simplest case, these pdfs can be understood as a most likely model together with an error bar (spread). We applied this technique to solve for elastic velocities and density in the lower mantle which can be converted into robust three-dimensional pictures of temperature and compositional variations. I will show that this identifies new structures in the lower mantle which have far reaching consequences for our understanding of Earth dynamics. A second example focuses on the anisotropic structure of the inner core. With the classical least squares inversion, a 20 year old dispute couldn't reconcile two independent data sets due to incompatible regularization. Our probabilistic approach found the most likely solution which satisfies both data sets. This new solution puts strong constraints on the solid state of iron in the inner core.