TF07 Snowmass Report: Theory of Collider Phenomena

11+11 pages, 343 contributors, 1 key formula; contribution to Snowmass 2021, draft report of the Theory Frontier topical group for Collider Phenomenology (TF07), comments and suggestions welcome ; v2: updated contributor listTheoretical research has long played an essential role in interpreting data from high-energy particle colliders and motivating new accelerators to advance the energy and precision frontiers. Collider phenomenology is an essential interface between theoretical models and experimental observations, since theoretical studies inspire experimental analyses while experimental results sharpen theoretical ideas. This report -- from the Snowmass 2021 Theory Frontier topical group for Collider Phenomenology (TF07) -- showcases the dynamism, engagement, and motivations of collider phenomenologists by exposing selected exciting new directions and establishing key connections between cutting-edge theoretical advances and current and future experimental opportunities. By investing in collider phenomenology, the high-energy physics community can help ensure that theoretical advances are translated into concrete tools that enable and enhance current and future experiments, and in turn, experimental results feed into a more complete theoretical understanding and motivate new questions and explorations