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1. There is increasing availability and use of unstructured and semi-structured citizen science data in biodiversity research and conservation. This expansion of a rich source of ‘big data’ has sparked numerous research directions, driving the development of analytical approaches that account for the complex observation processes in these datasets. 2. We review outstanding challenges in the analysis of citizen science data for biodiversity monitoring. For many of these challenges, the potential impact on ecological inference is unknown. Further research can document the impact and explore ways to address it. In addition to outlining research directions, describing these challenges may be useful in considering the design of future citizen science projects or additions to existing projects. 3. We outline challenges for biodiversity monitoring using citizen science data in four partially overlapping categories: challenges that arise as a result of (a) observer behaviour; (b) data structures; (c) statistical models; and (d) communication. Potential solutions for these challenges are combinations of: (a) collecting additional data or metadata; (b) analytically combining different datasets; and (c) developing or refining statistical models. 4. While there has been important progress to develop methods that tackle most of these challenges, there remain substantial gains in biodiversity monitoring and subsequent conservation actions that we believe will be possible by further research and development in these areas. The degree of challenge and opportunity that each of these presents varies substantially across different datasets, taxa and ecological questions. In some cases, a route forward to address these challenges is clear, while in other cases there is more scope for exploration and creativity.