I have also been using Claude for code review for the last ~6 months. In my opinion, it is extremely good on technical, localized issues but still limited when it comes to more global issues.
My usual approach is not to give it an elaborate generic CLAUDE.md, but to have a highly interactive session, usually going commit by commit: When I just ask it to review a PR carefully, there are many types of issues it won’t find - but when I combine it with my own knowledge and intuition to nudge it towards certain areas (which is very PR dependent), even if I can’t formulate it very well, it gets much deeper into things and will usually work out the details on its own and get to a solid assessment whether there is an actual issue with the code.
So my experience with code review is similar to what Terence Tao just said about using AI for math problems:
Additionally, a lot of AI companies have this obsession with push-of-a-button, completely autonomous workflows where you give your task to the AI, and then you just go have a coffee, and you come back and the problem is solved. That’s actually not ideal. With difficult problems, you really want a conversation between humans and AI.