Policy makers across the entire globe have repetitively expressed concern about climate change as a trigger of mass migration and increased political instability. Recent research on both climate-conflict and climate-migration linkages has gained significant attention in the scientific and public debate. Both research fields are deeply intertwined and share some common characteristics. They also have been rapidly evolving during the past years with major achievements being made. Perhaps most importantly, an improved understanding of the role of (potential) climate change impacts in migration and conflicts has been achieved, which has been essential for moving beyond environmental determinism toward a more nuanced exploration of the interlinkages between climate, conflict and migration. Yet, significant conversations and uncertainties continue to exist, hence indicating the urgent need for further advances in these fields. Here, we debate cross-cutting and common pitfalls in both research fields and their implications for policy and research. These pitfalls include (i) insufficient attention to context factors and causal chains, (ii) underestimation of complex spatio-temporal patterns, (iii) discrepancies between quantitative and qualitative evidence, (iv) the non-consideration of adaptation strategies, and (v) a narrow spectrum of methods. We illustrate best practices and suggest ways to move the debate forward.