The u-invariant of a field is defined to be the maximum dimension of anisotropic quadratic forms over the field. It is an open question whether every quadratic form in at least nine variables over the rational function field in one variable over a p-adic field has a nontrivial zero. Equivalently, is the u-invariant of Q_p(t) equal to 8? We shall trace the history of this question and sketch a proof of an affirmative answer to this question for nondyadic p-adic fields. More generally, every quadratic form in nine variables over function fields of nondyadic p-adic curves has a nontrivial zero. (Joint work with V. Suresh)