Abstract: To study the arithmetic complexity of a field which carries a valuation, it is useful to know whether the associated valuation ring is a(n existentially) definable subset of the field. If the valuation is henselian, then such definability can often be established under mild assumptions on the value group or residue field. Without assuming henselianity, however, no standard approach exists. In this talk, I will discuss how one can establish existential definability of non-henselian valuation rings, in particular in function fields. Special attention will be given to the role of modern local-global principles from quadratic form theory. The presented research was part of my PhD project and will appear as joint work with my former supervisors Karim Johannes Becher and Philip Dittmann.