The theory of Newton-Okounkov bodies assigns a convex set to a choice of a maximal rank valuation on a graded algebra. When this algebra is taken to be a section ring of a projective variety $X$, and the valuation satisfies a few extra conditions, this construction can be used to define a flat degeneration from $X$ to a projective toric variety. I will describe joint work with Kiumars Kaveh where we use tropical geometry to give a necessary and sufficient condition for the existence of such a valuation on a coordinate ring of a projective variety. I also discuss methods for explicitly computing this valuation, and illustrate the construction on a few examples.