Progress in particle physics research comes from the connection of physics motivation to high energy experiments. Several key mysteries such as the nature of dark matter and fine tuning in the Higgs mass underline the need for new physics at the TeV scale, and the Large Hadron Collider provides an essential probe for discovery in this regime. This talk focuses on novel LHC searches in unexplored phase space, specifically long-lived particles and anomaly detection, along with the associated challenges of such analyses and ways to address them via creative new tools. The High Luminosity LHC, the corresponding ATLAS detector upgrade, and studies for future colliders are all crucial for the longevity of these searches. These topics are discussed in the context of long-term planning for future experiments and the continued success of the field.