Argumentation occurring in public controversies (large, long-lasting, and complex disagreements) deserve more attention from argumentation theorists than they have yet received, primarily because they offer plentiful opportunity to discover new facts about the contemporary practice of argumentation. Drawing on the polylogue framework (Lewiński and Aakhus 2023) and the cartography of controversy (Venturini and Munk 2022), nine suggestions are offered for how to build new theoretical knowledge through observational research that combines classic techniques in qualitative social science with emerging computational techniques: (1) aim for observationally grounded theory; (2) anchor analysis in argumentative texts; (3) practice constant comparison; (4) build outward from individual texts to networks; (5) investigate the places where texts are produced; (6) pay attention to the literatures where texts accumulate; (7) leverage computational techniques for natural language processing of large bodies of text; (8) reserve judgment on matters of disagreement within the controversy; and (9) try team science. Recent argument-centered studies of controversies demonstrate aspects of this approach and show its promise for discovering interesting and novel phenomena.