Causal discovery aims to automatically uncover causal relationships from data, a capability with significant potential across many scientific disciplines. However, its real-world applications remain limited. Based on a systematic review of the recent causal discovery literature, we claim that current methods often rely on unrealistic assumptions and are evaluated only on simple synthetic toy datasets, often with inadequate evaluation metrics. We discuss how this problem should be tackled, first by presenting fields where causal discovery holds promise for addressing key challenges: biology, neuroscience, and Earth sciences. We highlight available simulated and real-world datasets from these domains and discuss common assumption violations that have spurred the development of new methods. We aim to encourage the community to use more realistic datasets and more adequate metrics.