Carbon capture, utilization, and sequestration have the potential to enable deep reductions in global carbon emissions if high storage efficiency can be achieved. A major hurdle to industrial-scale implementation of geological carbon sequestration (GCS) projects is the potential migration of fluids from the storage formations and the resulting legal and financial liabilities. The capability to accurately identify pathways by which stored CO2 could leak, has leaked, or is leaking from the targeted storage zone is thus of paramount importance to site licensees and regulators. Many monitoring, verification, and accounting (MVA) techniques have been devised over the years, however, pressure-based leakage detection remains one of the most sensitive and cost-effective technique for early detection of fluid migration from storage formations. It has consistently received the highest score in terms of benefit/cost ratio and it provides the greatest potential for leakage detection with broad areal coverage. Although much has been done in the area of forward modeling of leakage scenarios, the more challenging problems of pressure inversion for leakage detection, monitoring network design, and applications to operational GCS monitoring deserve more attention. Given the advent of permanent downhole gauges, which are real-time pressure and temperature monitoring systems installed at the bottom hole of reservoir wells, a salient question is how to leverage these infrastructure investments to reduce GCS risks caused by leakage from storage formations.