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. Current methods often rely on unrealistic assumptions and are evaluated only on simple synthetic toy datasets, often with inadequate evaluation metrics. In this paper, we substantiate these claims by performing a systematic review of the recent causal discovery literature. We present applications in biology, neuroscience, and Earth sciences - fields where causal discovery holds promise for addressing key challenges. We highlight available simulated and real-world datasets from these domains and discuss common assumption violations that have spurred the development of new methods. Our goal is to encourage the community to adopt better evaluation practices by utilizing realistic datasets and more adequate metrics.