This paper gives a comprehensive review of the **open problems** and future directions within the field of **mechanistic interpretability** (MI), which seeks to understand the computational mechanisms of neural networks. The authors organize these challenges into three main categories: **methodological and foundational problems**, such as improving decomposition techniques like Sparse Dictionary Learning (SDL) and validating causal explanations; **application-focused problems**, which include leveraging MI for better AI monitoring, control, prediction, and scientific discovery ("microscope AI"); and **socio-technical problems**, concerning the translation of technical progress into effective AI policy and governance. Ultimately, the review argues that significant progress on these open questions is necessary to realize the potential benefits of MI, particularly in ensuring the safety and reliability of advanced AI systems.