In a joint work with S. Baader, L. Lewark and F. Misev, we classify 3-braid knots whose topological 4-genus coincides with their Seifert genus using McCoy's (un)twisting method and the Xu normal form. We also give upper bounds on the topological 4-genus of positive and strongly quasipositive 3-braid knots. In the talk, we will define the relevant terms and provide some context for our results.