There are many articles on the web about how to do good code reviews, with mostly all of them either discussing their merits or how to obtain maximum value from them.
In a new role I've recently helped introduce and roll out the agile process and to start with as part of each story we always added a task to "code review" all work. We made sure that differences from source control were used to make sure only the changes made were reviewed, made sure that everyone had chance to partake in reviews so it wasn't just one or two people providing all the feedback on the other team members work. It worked well, the reviews were productive and provided really good feedback for everyone.
But there was something about them that didn't feel right for the entire team, but it was the sprint planning process of tasking the stories that gave us the answer to what was bothering us. For every story we added the code review task to the END of the story, which of course by it's very nature was when all the development had been done! We analysed most of the feedback that came out of the review process and realised that, similar to the wedding singer, that information would have been useful to us "yesterday".
So as a little experiment we added a task right at the beginning of the story that involved at least 2 developers, sometimes a tester and for more complex stories, the entire team. Outside of the task planning session the developer(s) assigned the task spend 30-60 minutes detailing the approach they intend to take to solve the story - the other participants in the process get to question the approach and by the end of the discussion we've normally ironed out all the bumps. During these experimental stories we kept the code review task, but the initial discussion task along with taking a TDD approach coding against Gherkin provided by the test team we quickly identified that the code reviews had become redundant.
We've now taken the decision to remove the code review task completely and haven't noticed any decrease in code quality or maintainability. The number of issues reported in the produced code has stayed pretty constant, but we're no longer have to spend any time at the end of the story reworking any code as a result of review feedback!