Assessing and shaping the effects of artificial intelligence (AI) and machine learning (ML) on climate change mitigation demands a concerted effort across research, policy, and industry. However, there is great uncertainty regarding how ML may affect present and future greenhouse gas (GHG) emissions. This is owed in part to insufficient characterization of the different mechanisms through which such emissions impacts may occur, posing difficulties in measuring and forecasting them. We therefore introduce a systematic framework for describing ML's effects on GHG emissions, comprising three categories: (A) compute-related impacts, (B) immediate impacts of applying ML, and (C) system-level impacts. Using this framework, we assess and prioritize research and data needs for impact assessment and scenario analysis, and identify important policy levers.