Heat and flooding are frequently cited as among the deadliest and costliest climate hazards, respectively, and both are intensifying due to urban developments and climate change. In response, many cities worldwide are increasingly turning to green infrastructure (GI) to mitigate climate risks such as extreme heat and flooding while enhancing overall resilience. However, existing research suggests that knowledge systems for GI globally have significant gaps that undermine the effectiveness of these investments. These include a narrow focus on limited functions while neglecting others and a lack of research on the decision-making processes that determine which GI functions are prioritized and where. The metrics and models used for siting GI likely shape its effectiveness in managing stormwater and mitigating heat risks in urban settings as well as who benefits from GI investments. This study systematically reviews the academic literature on GI spatial planning worldwide to analyze the GI types, indicators, and methods proposed for siting GI to address heat and stormwater challenges in cities. Our findings reveal that the spatial planning of GI for heat and stormwater remains largely separate in the academic literature, despite widespread calls for multifunctional GI. GI siting for stormwater management has a more robust and consistent body of literature with similar methodologies compared to that for heat risk mitigation, and the types of GI used differ between the two focus areas. This study provides valuable insights that can inform more integrated and effective approaches to GI planning, enhancing urban resilience to climate hazards.