One day I joined a team maintaining a huge, legacy, and slow Rails app. We thought that we have to optimize the application throughput for the user happiness, and so we formed a task force that focuses on the performance.
Now, here's the record of the team's battle, including how we inspected and measured the app, how we found the bottlenecks, and how we tackled each real problem, about the following topics:
Tuning Ruby processes
Finding slow parts inside Rails, and significantly improving them
Fixing existing slow libraries, or crafting ultimately performant alternatives